Statistically, cyclists break the rules at roughly the same rate as drivers, in even the most unfavourable studies.

But there's a key difference. When cyclists break the law, it is generally done in the interest of their own safety, because the law is often set up in such a way that following it, for cyclists, actually puts you at more risk. Drivers tend to break the law merely for convenience. And when a cyclist does hit someone, the impacts are much, much less bad than when a car does.

You're proposing a solution to a problem that does not exist. And which would have far more intense negative side effects, because it would decrease the number of cyclists. That is precisely the opposite of what good policy does.

Not to mention, having plates doesn't actually work to stop cars breaking the law and deliberately endangering people's lives all the time. You can send clear video footage to the police and you've got maybe a 1 in 10 shot at best that the police actually fine the driver.