This idea probably has it's pros and cons, as do all ideas...
But, what about free, easily accessible, open all hours, driver enjoyment facilities... Like an area where you can go and take your friends / car for a strap without having to worry about power poles, bumps in the roads, police, pedestrians, etc... Like an open all hours skidpan / circuit / drag strip / donut pad... With runoff areas and all the other necessary safety precautions...
If I wanted to show off my car to someone, and I had the choice of doing it at a facility like the above, or on the street in a 50 zone with all it's inherent dangers... I know what I'd choose...
No need for power restrictions, no need for curfews, no need for multi level licensing, no need to do it on the streets...
Or we could just give all new license holders 350rwkw RWD monsters and let the wheat sort itself from the chaff