More seriously, while the benefit to people with arthritic knees, gouty toes, metal hips or just plain loads and hills, is obvious when it comes to having a battery to provide extra power, I do wonder about the larger effect. If you don't have to do any pedalling, in what way is it different from a petrol-burning scooter? It's slower and quieter.
Slower and lighter. Noise doesn't hurt people, mv
2 does.
Put it another way, how is a complaint EAPC or Pedalec different from a pedal cycle?
Slower than some, faster than most. Lighter than some, heavier than most
[1]. Noisier than some, quieter than most. I don't think there's a lot in it, IMHO. Out riding with barakta, the main difference is which of us is faster on what gradient. She whizzes up hills (relatively speaking), but it's easy to exceed the limiter on a gentle downhill (as a fitter cyclist, I regularly do on the flat), at which point you're doing all the work yourself.
You could invoke the cycling purity argument, but I don't think that has any place in road legality. You might as well ban recumbents because they're 'cheating', or Chris Hoy because his legs have a power rating in line with a motorcycle.
I guess UK is probably a bit of an oddity in considering a moped to be more like a motorbike than a pedal bike, though. When I lived in Paris, mopeds didn't have registrations. Neither did the very popular microcars (like a four-wheeled moped) which meant they got parked in all sorts of ludicrous places. But that was in 1989. Nevertheless, I do feel that allowing electric power without pedalling does put a toe across the line.
Yes, I see electric assist cycles filling the void left by the illegalisation of practical mopeds, and as a practical alternative to Class 3 invalid carriages. They're cheap, easy to park, gets you where you're going in reasonable time and doesn't require undue physical effort even if there are bastard hills in the way. As a bonus, they're fairly safe and don't belch fumes.
Providing a power boost to Cyclists who need one is an edge case.
[1] Though as usual this is dwarfed by the variation in rider weight.