Nice idea, but you need the safe 19yos to subsidise the dangerous ones.
For example, 1000 teenagers insure their cars for a total revenue of £2m. 10% of those make a claim with an average cost of £20k, meaning the insurer breaks even.
If they only charged the accident-free drivers £400 then the total revenue would be £560k and the insurer would be making a huge loss. To break even, they would need to charge the dangerous drivers £16,400. Basically if you had an accident you wouldn't be able to drive again until you were 25 unless you had loads of money.
Even with the current system this is a problem. I know a female driver under 25 who had a slow speed collision with a push chair. The police put the blame firmly with the mother (checking that the road was clear for herself and forgetting that she had a push chair sticking out in front of her), but the mother is seeking compensation for the child's injuries. As such my friend is not currently driving, and has had to turn down jobs because they required you to operate your own car.