For insurance premiums to come down noticeably, there has to be a total overhaul of how the insurance system works. I'd prefer a system where every 'driver' was forced to have third party insurance. Car owners could then chose to take out more comprehensive cover for their car, much as they do now.
I must be missing something because you appear to have just described the current system. Third party insurance is already the legal minimum requirement for a driver, and they can choose to pay more for fully comp? The only thing is how do you "force" a driver to get insurance?
The only way it would work is insurance through the cost of fuel.

So electric cars don't need insurance?
One point on that fraud reporting site was interesting:
The only way it would work is insurance through the cost of fuel. You pay for what you use. A higher performance car generally uses more fuel. Perhaps add in a rebate system for lorry drivers?
The only way to force them is to take 3rd party insurance as a basic tax on your wage.....
Clearly that won't work because all the council estate scroungers who don't work won't be paying tax......