Interesting idea but I don't think that this would improve the current situation by much.
Firstly implementing a driving test and then having every new user complete it would be an enormous logistical challenge and take years to develop and flesh out. And what would we even want to test for? Driving in a straight line, following a road for 600km without swerving, basic road laws?
Some of those criteria we could test for would be impossible to automate and therefore require human examiners. This just wouldn't feasible with the amount of new users joining daily.
Secondly, I think that this doesn't fix an underlying problem. Many players don't just ram into you because they are bad at driving but rather more because they do it intentionally. Those types of players would just complete the "Driving Test" with as much effort as needed to pass and once they are in the main game start crashing into everybody and wreak havoc.
The only real upside I could imagine is, that some trolls are just out for quick laughs and would get discouraged by having to complete a "Driving Test" and potential lessons.
This discouragement would of course also have an effect on real users who would never get to experience the multiplayer because they don't have the time and patience and just start playing some other game with their friends.