The vet world is extremely small. Everyone knows everyone. Actively poaching customers is just not the done thing. You cant go after Jims customers from his practice 30 miles away because you probably trained alongside him yourself and the conversations that local Golf club or outside Private school when you bump into him could get awkward.
I reckon the larger farms will eventually club together and pay enough to employ a vet and his assistant if corporations intend to rob the job.
As for private hospitals, IVF clinics and the like the majority of them are privately owned anyway.
A big corporate I know recently put out the offer '50% off your first surgery with us including drug costs' if you switch to them at a newly opened branch, it may not be the honourable thing but it is being done.
I couldn't name a single vet who's children go to private school either