My vet is really experiencing this now - they have been advertising for another associate vet for about 6 months now, and as far as I know, haven’t had any good applicants. Meanwhile, they are booking spays and neuters out 2 months AND trying to take new clients. Just a couple of weeks ago, I was there when a couple brought in their dog. They were from 50 miles away. Said they had gone to their local vet, sat in the waiting room for four hours, then were told the vet couldn’t see them that day, AFTER making an appointment. So they decided to go to my vet instead.
My vet has gone to doing walk-ins only on Saturday. The first 20 - 25 in the door get in. Clients start lining up 30 minutes before they open. Those are usually vaccines, etc. but the occasional emergency comes in (like me), too.