I think part of the issue is the driving test itself. I'm not an advocate for making it harder par se, but there is no motorway driving, no skid training etc, and no fire department involvement in showing the aftermaths of a horrendous crash, built into the driving test (that I'm aware of ?). For all new drivers, the first time they do high speed motorway driving is after they have passed their test, and skid training the first time they loose control in the winter ice.
I agree to a point in what Bear is saying, however I've know 40 year olds with less common sense than a 16 year old, so think it does hugely depend on the individual. Perhaps better would be a tiered system like in some European countries, where regardless of a young person's ability to afford any car he wants (and the insurance), perhaps the HP of the available cars should be limited for the first 3-5 years of driving, slowly increasing in power if the driver has no accidents or points.
With regard insurance prices, well that's a tricky one. Insurance companies are no fools and will therefore charge what they think in proportion to the risk - hence young inexperienced drivers get charged more than old experienced farts like me. The problem with that, is if the insurance premiums get ridiculous, say £3-£5k upwards a year, with the resulting fines levied by the courts (or lack of them) for uninsured drivers, it would therefore be a gamble worth taking for some to run with no insurance, and take the risk of getting caught. Even if you are caught, a typical £250-£500 fine more than outweighs a £7k insurance cost. So I think insurance companies should take a fresh look at how they calculate their premiums, to avoid encouraging many people to take this gamble.