One thing the BiB in Thailand don't have to be is reasonable. If they can raid large crowded bars and drug test everyone there, then I don't see why they can't block the sois and check every one of the motorbike maniacs to see if they are holding a valid license, if they even have a helmet, and if their motorbike is parked in an illegal manner. While they're at it, drug test them too. I don't think it is farfetched to find out every one of them are illegal.
If they try to claim they didn't rent a motorbike, fine. Confiscate any unclaimed motorbikes along with the ones that for whatever reasons were also confiscated.
Without some sort of very aggressive drastic action, maybe even draconian, action, this is not going to stop.