When I was on my P's I was legally allowed to drive whatever I wanted. However, I spent most of my time on P's driving a stock FWD ford laser...
Looking back over the years, my cars have gotten progressively faster - not just in terms of HP but also in terms of the brakes, suspension work, that has been done. From the laser through various stock and modified N/A R31s, to the fairly stock wedge, to the wedge as she is now.
This has probably been more to do with the amount of money I had to spend on cars at those points in my life, rather than through any sensible decisions I have made or through laws forcing me to do it. The only sensible decisions I can really take credit for is probably always doing the braking/handling mods before the power mods.
However, I feel that the way my cars have progressed has meant that the car I am driving has been appropriately matched to my skill and confidence as a driver, and as these have progressed so has my car. I mean, if I had been driving the wedge as she is now when I was first on my P's, I most probably would have killed myself.
P platers, much as they like to think they are, are not driving gods. They have very limited experiencing and just because they can pass a driving test doesn't mean they can handle a sports car on the edge. Sports cars, driven hard, will tend to get you into trouble. That's the nature of the beast. Good sports cars will get you OUT of trouble just as well, IF you know what you're doing.
It takes time and experience to learn how to respond when you get into trouble, and while I certainly don't claim to be a driving god now either, I can say with some confidence I am a much better driver than when I was on my Ps...
So long story short, yes I think there should be restrictions on what cars P platers drive... I don't think the current rules are perfect - they could definitely be improved, but in principle I agree with them.
I don't think there should be a distinction between N/A and forced induction - a powerful N/A car will get you into just as much trouble as a powerful turbo car. A blanket HP limit combined with a power to weight limit, applied to all cars not just forced induction, would work well.
I don't think we need to stop P platers from modifying cars, if they want to do brake and handling upgrades why shouldn't they - as long as they do them legally and engineer them properly. And HP mods are OK too, as long as they keep to the power restrictions.
With all that said, more driving training would definitely not hurt either... you still can't fast track experience, but more training can give you a step in the right direction.
/rant