If the PE firms buy up the practices and put all the vets in the area under a non-compete (not a hypothetical; see my other comments in this thread, it happened here in Rochester NY and is widespread practice), there aren't any vets to open a competitor.
Veterinarians are not a dime a dozen. You can't go to a boot camp and emerge in 6 months with a license to practice. They should all simply refuse to sign non-competes (not that they should be legal in the first place).
There is not an infinite supply of vets, especially those free from debt and who can borrow enough to start a practice.