My question on this is: does your rabbit have what is known as "wolf teeth" and the teeth grow all screwy or misaligned? This is an inherited condition called malocclusion and you should not use this rabbit for breeding stock. Also, you shouldn't have to take your rabbit to the vet at all for teeth trimming, you're paying for something easy to do yourself!
Rabbit teeth grow about 1/2 inch per month and this is NORMAL. I would not remove the rabbit's teeth completely. Seems an inhumane thing that would cause more nutritional/digestive problems for the rabbit than regular trimming. So, if the rabbit's problem is chronic, get a pair of dog nail clippers - the kind with the scissor action and the semicircular blades. You can trim the teeth yourself, just firmly wrap the rabbit in a towel so he can't hurt himself or you or escape, and hold him on his back and trim the teeth. Another thing to note is if a rabbit breaks a tooth by random chance, the opposing tooth in its mouth can grow very long as a result and need trimming until the other tooth grows back. It's something to watch for.
I give my rabbits plenty of hay and a few of them have grey chewing blocks from the pet store to chew on. For 99% of my rabbits, this is plenty sufficient to keep their teeth in good order. You can also give them sticks to chew on, just make sure you lookup the species of wood first and ensure it is not poisonous to them. Many of my breeding does and their babies chew on their nestboxes since I make them out of wood. I have only ever had one rabbit born with a case of wolf teeth. It was so bad the rabbit had to be culled as it couldn't eat. We'll be watching future litters from the same parents and should the wolf teeth recur again, the rabbit with the bad gene for it will get retired from breeding.