That ^2 is a load-bearing exponent which changed my entire perception of safety.
With the oil crisis making it a good time to buy an ebike, I see the same problem popping up on bike forums that I faced when making my original purchase. At least here there's the option between a Class 2 (32kmh max, usable on paved trails) or a Class 3 (45kmh max, limited to roads). When I bought my first bike I got a Class 3 because I'm getting 40%~ more speed for the same price. I could arrive at my destination 40% faster than I do on my cargo bike.
Assuming a rider+bike weight of 100kg and converting the two to m/s: 8.89m/s, 12.5m/s-
Class 2- 0.5(100)(8.89^2)= 3950 Joules of energy. That's what you experience when crashing at max speed, the equivalent of falling off the roof of a building with one floor.
Class 3- 0.5(100)(12.5^2)=7,810 J.
Despite the speed only increasing by 40%~, the kinetic energy you experience in that crash almost doubles. The energy your brakes have to absorb to stop, and with that the stopping distance and wear, almost doubles. Your risk of fatality jumps significantly. You are now jumping off the tallest house in your neighbourhood and that is the level of injury you can expect from the slightest mistake.
If you or anyone you know is tempted to get a hyperbike because it goes much faster than a cargo bike, especially beyond the Class 3 speeds that I don't even want to think about the injuries from, that impact force needs to be a primary consideration. I am confident that with proper safety gear I have a 90% chance to survive a crash with injuries that won't last a lifetime. If my cargo bike was Class 3 instead of Class 2, I could not maintain that same level of confidence. It's such a minor difference when you are looking at generic speed numbers but you will crash and that is the standard you need to prepare for.
Buy a Class 2 and maximise your weight-bearing utility over speed. Slow is smooth and smooth is fast.
Originally I made this as a comment on /r/ebikes. The part I didn't copy-paste here is that I normally ride at around 24kmh, decreasing to a 10kmh or slower crawl around anyone I have to pass. On my 15 minute commute that might cost me up to an additional 5 minutes. But I spend those moments smelling flowers, watching birds, and doing other things that make that time enriching instead of stressful.
(0.5)(100)6.67^2= 2224.4 J. If 3950 J is a 100kg weight falling from a 4m one-floor building, now I'm falling from a 2.2m doorway. My padded jacket is enough to avoid a bruise instead of a broken arm.
edit: Not to say that 32kmh is without its merits. I think that's the perfect balance between urban speed and safety as the equivalent to what I'd drive on the adjacent streets. I can react and stop fast, crash relatively safely, and save a couple minutes over driving+parking. It feels as fun as driving 70kmh on nearby winding canyon roads.
I agree with your post, but I think the power is the class 3 is very useful when used in the proper situations and the proper respect for the speed (as you described).