And this is the problem. People who have their license suspended often drive anyway. Sometimes they have to in order to get to work because the U.S. has a shit public transportation system in vast areas of the country.
Give insurance companies the will power to say no im not going to insure you. And then cap insurance rates. and by cap i mean no insurance should be more expensive than the rate new drivers are allowed to be charged.
Where i live insurance rates have a discount for being a good driver. Goes up each year to cap at about 40percent. This is tied to your liscence not insurance.
Increase that discount for good drivers and make sufficiently bad drivers unable to be insured.