The truism that "speed kills" is, well, true. Bicycles may be unsafe at any speed, but that is true for any form of transportation. The question is "what is a sane and safe speed where the benefit of getting somewhere exceeds the risk of death and injury related to trying to get there too fast?"
What is legal is not necessarily a sane guideline. In America and elsewhere, cycles are just another vehicle and must obey the posted speed limit on roadways. If the speed limit is 15 mph in a school zone, a cyclist going faster can get a speeding ticket. But if the posted speed limit is 75 mph (120 km/h) on a highway and a cyclist is going downhill, 75 mph may be the legal speed limit, and the cyclist won't get a ticket for going 75 mph, but going 75 mph on most bikes is not a reasonable speed. It has been done, some daring doers live to tell the tale, but what is legal is not necessarily prudent, so reject the legal and come to your own senses about what is a safe and sane speed.
A typical cyclist, as observed in the wild, goes about 9 mph (15 km/h). Why? Because they are average cyclists who can output 60 watts of power for a significant period of time. Average cyclists are not, however, average humans who are good for about 20 to 50 watts. In the Netherlands, the country with the most avid cyclists, 25% of trips are by cycle pedaled by the more fit, while in the USA, only about 1% of trips are pedal powered, possibly because only 1% of the adult population can sustain a 60+ watt output. Cycle use varies as does fitness.
In Europe, typical e-bikers have been observed to go 13-14 mph (22 km/h), which is a speed more typical of a very fit human-only powered cyclist (see Limits of Human Power). Tour de France cyclists average 25 mph (40 km/h). Does it reasonably follow that e-bikers who can afford a big enough motor/battery should also average 25 mph? Or (if they feel like it) 35 mph? If in order to average 25 mph it is necessary to go 50 mph at times, then 50 mph may seem reasonable, so....? If it feels good, do it? Should e-bike riders recognize no limits other than (if they feel like it) the legally posted speed limit or whatever speed full throttle allows?
On bicycle paths that may include joggers and pedestrians, a speed limit of 15 mph is commonly posted. Cyclists going over 15 mph are a hazard to cyclists going the typical 9 mph, not to mention pedestrians and their pets, just as on roads fast cars are a hazard to the fastest cyclists.
A speed limit of 15 mph on multi-use bi-directional pathways is arguably too tolerant. In China, where cycle use is common, the speed limit for bicycles and e-bikes is 12.4 mph (20 km/h). The speed limit for e-bikes in the UK and Europe is typically 25 km/h (15.5 mph). In most of North America the speed limit is 20 mph (32 km/h), though many e-bikers go faster because....speed is good, gooder, and more good.
Typical American e-bike enthusiasts chafe at (or laugh at) any suggestion that a mere 20 mph speed limit should be considered. They tend to think a 20 mph average speed may be reasonable, which implies an absolute need to go 40-50 mph at times to make up for times spent at stop lights. Although 750 watts is the federal legal limit for e-bike use on public roads in America, those who say they will only ride on private property can buy the most ginormous motor their bike can carry. To go fast, they have to over-amp and over-volt (mere 72 volt systems may be acceptable) to produce enough power and speed to sometimes satisfy.
As a study in the American Cycle Zeitgeist, consider the super-bionic-human offerings of Outrider USA's electric trikes. Winning the Pike's Peak Pedal Electric Hill Climb by setting a new record speed creates interest—averaging 32 mph (51.5 km/h) going uphill all the way is a good start. When not climbing mountains, the 422 Alpha Trike (as in Alpha Male with huge cajones) can do 40 mph on the flats. The American response, conditioned by decades of oversell, is "What's not to like?" and "Gotta have one." To mention that the 4,000 watt motor and 20+ mph speed renders the trike illegal (not to mention unsafe) off the race track in all 50 States is merely to comment on the insanity of laws that interfere with the sacrosanct American pursuit of power and speed. To make a grinning concession to legality, the trike has a low-speed button that limits the power to 750 watts and speed to 20 mph which means it could be used for a few seconds to go from 0 to 20 before being turned off. Of course 4,000 watts is minimal for safety, right? To ride in traffic (at least off freeway) you have to keep up with it least the bigger boys run you over, so gotta be able to go 40 mph just to be safe..........(cue endless rationalization)..........and so 6,000 watts would be better. As a light e-motorcycle, great product, but calling it an e-trike is a misnomer.
To those not prone to maniacal laughter, 15 mph (25 km/h) is enough. A combined human and e-motor power of 150 watts is enough to make bicycle technology work and work well to meet much of our transportation needs. Although a 250 watt e-bike can go over 15 mph, the throttle need not be cranked to max when not at a dead stop. If an e-motor allows unfit humans (over half of industrial society humans) to be active cyclists, then 9-10 mph is enough. Those who start out at 20 watts plus 30 to 130 e-watts as needed will gradually become 30 watt humans, and becoming 50 watt humans is an obtainable goal. If there are no steep hills or strong headwinds, 75 watts to 100 watts is enough to get around. A total power of 150 watts is only needed on occasion. At times a low-power human will not need to use an e-motor at all, and often 50 e-watts of assist will be enough. The temptation to throttle up until the throttle can't be turned anymore while not peddling is there, but therein lies ill health and an increased probability of sudden death, not to mention a ban on e-bikes.
Those who nearly have enough human power to cycle the distance and climb the climb have designed low power e-assist cycles that offer up to 100 watts of e-assist, which is power enough for some. The designer admits that 150 watts of e-assist might be reasonable, but 100W+ of human power is assumed. For those requiring total e-assist at times, 250W may be enough. If the rider is overweight and thar be hills about, a 500W motor is reasonable. To power a loaded Winnetriko with trailer while touring continients, 1500W should be enough. So for "power enough" think 100W to 1500W of motor power, meaning the 165,000 watts offered by an average car is possibly more than enough.
E-bike commercials that want to sell the public on the idea that e-bikes, e-bikers, and e-biking is all good, (see Time Warner/Pedego commercial) show all the bike riders, mostly all responsible looking elderly, blissfully pedaling/coasting around at about 5 to 8 mph, which is to say looking exactly like non-e-biker dudes on regular looking bicycles. No red flags here. Commercials trying to sell e-bikes to would-be ebiker dudes show all the sporty up-scale riders zipping along at high speed grinning maniacally while not pedaling.
The trouble with e-bikes is speed. With ICE bikes the trouble is all about speed and noise. With e-bikes it's all about the speed. If there are enough of them in an area going faster than regular, average bicycling sorts, they become a problem and they will get regulated. To blend in with bicycles the speed limit would need to be about 15 km/h (9.3mph). The alternative, increasingly common because it works (unlike posted speed limits), is to ban them. Where e-bikes have not been banned, it is because there isn't enough of them yet.
Basically what makes an e-bike a moped is its speed. If it goes noticeably faster than a bicycle that an average person would ride in recreational mode (as shown in commercials) then it is not a bicycle. Only the very fit to athletic can pedal a purpose made bike at 20 mph for more than a few minutes and if they do so on a multi-use path, they are going too fast. It is only because there are so few who are fit enough, and fewer of them who actually go too fast, that regulating bicycle speed, other than banning them from sidewalks, is a non-issue most of the time. If 50% of bikes are e-bikes that anyone who can turn a throttle could (and most would) go too fast as is their constitutional right (see Article 7334) and because it says so right there in the Bible (somewhere).
If bicycles went at walking speed on sidewalks, there would be no reason to ban them. But asking bicyclists to go 3 mph on sidewalks, if it was ever tried, didn't work and so all bikes are commonly banned because there is no way to make them go slower than they can be pedaled. E-bikes, wanting to use bicycle infrastructure, that can go faster than average bicycles will be banned too unless there is a speed cut-off on the assist provided tied in to speed.
The alternative to being banned is to go EU and require "e-bikes" that want to be treated as bikes to stop assisting at 25 km/h (15.5mph) which is an experiment in progress. If 25 km/h is too fast, it may have to be lowered if there is too much mayhem when e-bikes reach 50% of the bike population. On multi-use paths, 25 km/h will likely be found to be too fast and the posted speed limit may be 15 km/h (9 mph). E-bike compliance by throttle alone would be low to nonexistent. E-bikes may have to be required to have a "multi-use path" mode, as indicated by a red light on the motor/controller, that means maximum e-assist is now 15 km/h instead of 25 km/h, so if rider is going over 15 km/h, they are getting no assist. Or DD e-bikes going too fast could go (oh the horror) into regen mode. Or all e-bikes can/will be banned. Arguing for no speed limit is to argue you are riding an e-motorcycle, since riding like the happy people in the commercial would be intolerable to an e-motorcyclist. Nothing wrong with riding/wanting an e-motorcycle. They just are not e-bikes, shouldn't be called e-bikes, and should expect to be regulated accordingly.
Hot roding e-bikes by using up to 22,000 watt motors has been done, and performance on a test track my amuse some, but if a practical low-power vehicle user expects to co-exist with human-powered vehicles, then "low-power" should be equivalent to typical human-only speed. Typical fit-humans who cycle put out 60 to 100 watts, while the very fit can sustain 150 to 250 watts. Athletes can manage 350 to 450 watts, but they are far from typical. Imagine an overweight grandmother speeding past the spandexed athletes without peddling. Now imagine there is something wrong with this picture. On a test track, no problem, but if e-cyclists expect to be tolerated by cyclists, they need to stifle themselves, as in moderate their use of e-power.
The fact is 250 watt maximum motors are fine under most conditions. If 250 watts is the legal limit, then a through-the-gears mid-drive motor would be required to handle long steep hills. There may be times when powering up a steep hill is preferable to getting off and pushing, so a 500 watt or even 1500 watt maximum direct-drive motor could be justified where hills are common, and high weight or really long steep hills implies more watts may be needed. If no steep hills are lurking about the neighborhood, a 250 watt motor is a reasonable choice for a direct-drive hub motor, so 250 watts, 350 watts, and 500 watts are reasonable assuming maximum wattage is seldom used. If an e-motor allows low-watt humans to cycle at 10 to 15 mph (15 to 25 km/h), then that's much preferable to zero (99% of American adults ride at zero speed since they don't ride bikes). E-bikes are to enable people, and going 15 mph is enough. If it's all about more speed, you end up with an e-motorcycle or Tesla. Consider resisting the Siren call of "MORE IS BETTER", the alternative being to live a life of "enough". Or get an electric Harley-Davidson whose speaker system alone pulls enough wattage to power a real e-bike.
Per one study, of those who get e-bikes to help enable themselves, 93% ride them at least weekly, up from 55% who rode regular bikes before getting an e-bike, and 73% used them to go different places than before. Reasons for getting an e-bike: 60% needed one to get up hills in their area, 65% used them to replace car trips, and 59% needed one because they suffered reduced ability to ride a standard bike due to disabilities (getting old is a disability so everyone becomes disabled over time).