Actually, we already have similar laws in France, as the US do by the way.
Each time you commit an infraction, you lose "points" on your driver license (the bigger the infraction, the higher the number of points lost). When you do not have any point left, you lose your privilege to drive. I currently live in the US and there are similar laws here too. Too many infractions in too little time and your driver license will be suspended.

So, no, government do not seize your car (it is your property after all), but they can revoke the privilege to use it on public roads. Similarly, this law revoke your privilege to access the internet. Burden of proof is a little lower (and that will be the problem), but the principle is already firmly entrenched in all modern society.

Driving or access to the internet are NOT rights, they are privileges and as such, they can be revoked.

Now, I am not saying this law is either just or well phrased or even that it will be enforced equally, just that your analogy is actually a lot more real than your realized.