This is an outstanding policy. I've been hit 3 times by uninsured drivers (in TN). The last time, my insurance company paid up and went after the deadbeat. He really was a deadbeat - had nothing, so the insurance company couldn't recover. Guess what? Right, my rates went up the next year.
I say tow the car immediately if they have no insurance. Put it in the system against their driver's license. If they get caught a second time, revoke their driver's license.
I have an even better idea. Do all the above, and then SHIP THEM BACK TO MEXICO, without the car.