Yet a full car license grants the right to ride a 50cc moped without any further test
Not so any longer. At one time to popularise mopeds the government permitted car licence holders to ride P1 class 30 mph restricted mopeds. That didn't last long, ending on 1st February 2001 and any newly tested car drivers in the 12 years since and the future have to go through the full P1 moped driving test procedures, including CBT.
However, the point isn't relevant, a car driver has been tested for competent road use and that is what the driving test is almost entirely for. And of course there is the question of insurance to protect third parties which so many conveniently ignore. As I've pointed out before, when speed rises above natural human speed capabilities the degree of injury damage rises sharply, so insurance cover is essential. Any law imposing insurance on e-bikes will have to be accompanied by e-bike registration, number plate and a driving licence for the law to be administered and enforced.
I'm sure hardly any e-bike riders want all this, which is why I say anyone thinking of asking for higher assist speed limits really needs to think through what that entails.
N.B. Crossed with Garry's post.