That's not 100% accurate. When you go to DMV you sign a form stating "you will maintain insurance". That's it. The police are using plate scanners yes and they flag all kinds of things like outstanding warrants etc.... but they are not cross-checking with Geico and the likes databases. If you have a link the states otherwise, I'd like to read that.
In my state they do. Not trying to share where I live but apparently they also do the same in Georgia. https://dor.georgia.gov/motor-vehicles/insurance/registration-suspension
Yep. It would appear you're correct. If you don't pay the insurance, they inform GA DMV, the registration gets suspended, and the automatic plate readers that do dozens of cars/minute as a cop just drives around see's yours and starts beeping. You're done. Here come the fines. The hole gets deeper.