I wonder if insurance would be a partial solution? Allow/encourage providers of liability insurance to raise rates on people with tickets, unless they are to the electronic limit.
Without better mechanisms to actually meaningfully enforce insurance requirements, changes to those requirements are unlikely to be effective.
The elephant in the room in the US is that although driving is a (very dangerous and extremely socially-costly) privilege, any attempts to hold drivers accountable and take away that privilege from repeat offenders is treated as a rights violation, so instead we just accept many deaths of innocent people from repeat DUI and speeders.
The profits stay within the government, fees can be easily adjusted to inflation and is enforced onto everyone thus reducing the headache for drivers and cops.
When you say a lot, by how much really? I suspect it's tiny.
I think if you're the sort of person who would drive with a suspended license you would also drive with expired plates and no insurance.
Maybe in this case it could work like child support: you pay the state, the state pays the insurance on your behalf, and if you don't pay the state then they're the ones coming after you.
At some point you might have to decide between letting the state garnish your wages, or giving up your car.