If riding a bike was as common as a car it'd be regulated all the same.
You already see "certain demographics" that suspiciously always seem to feature prominently in any given decade's policy failings screeching about how e-bikes need registration because they let people they don't like have easy geographic mobility.
Nope.
Regulation of cars , like anything, is expensive. It’s worthwhile for cars for safety reasons, but bikes are cheaper, and also way less dangerous in general, so need a lighter hand.
The current cutoff in EU is probably right, above a certain power level, e bikes are l, broadly, treated an motorcycles (licensing, type approval, insurance etc) , below that and with non-e bikes, is really just about the basics, eg are the wheels firmly attached and do the brakes and lights work?
Edit - I don't mind paying for the service. Maybe charge everyone $99 to file a case to avoid everyone piling on, but it helps resolve most egregious ones, and fee could be refunded at the agency's discretion.