It isn’t correct to equate frequency with overall risk.
One single car jumping the red whilst you were crossing in 20 years would have caused you much more harm if they had hit you. Cyclists jumping reds, whenever they do it, are unlikely to hit you, because they are smaller, more agile. If they do, they are less likely to injure or kill you because of the weight and speed.
I’m not saying it’s right to jump lights in any vehicle, but overall, cycling is much less dangerous to society than car driving.
Allocation of public resources on harm reduction is done by looking at the problem at a societal level. That’s why an expensive, hard to administer and all but impossible to enforce cycle registration scheme won’t happen.
The bad actors would still be bad actors - see illegally modded cars, unlicensed and uninsured drivers for an example of how it doesn’t work in motoring.
The plates would be either so large they are unsafe or so small they are unreadable by ANPR systems.
Any extra barriers to active travel will have negative affects on overall health, costing the NHS more money.
Enforcement won’t happen - see all the drivers on mobiles or jumping reds.
The junction you mentioned - does it have cameras? Do you think all the drivers who jumped ‘just a little bit’ on red got points and a fine? Doubtful - so how would it work for cyclists?
Someone has to install, maintain and monitor the cameras, then send the letters and collect the fine - or maintain the computer systems that automate it. If they aren’t spending that money on cracking down on motorists who actually kill and injure in the thousands every year, do you honestly think it’s available for cyclists who are 1/400th of the problem?