I suspect that the most beneficial result of the 3' law is that it will be easier to prosecute in the case of a collision, since the driver will, assuming that it can be proved it was his fault, be automatically in breach of the law.
I understand that, in many places in continental Europe, such collisions are automatically the fault of the drivers, unless they can prove tht the cyclist swerved violently. Of course, in France, for instance, the overtaking margin is supposed to be 2m, wich makes it highly unlikely that the rider swerved that much.