There are 10 vet practices in your city. 7-8 get rolled up into one uber practice by a PE firm.
They now have far less overhead per patient. Billing, equipment and even vets can be amortized over far more patients.
You, the hold out clinic, are now more expensive, or have a far smaller profit ratio, thus you are operating at a big disadvantage to the other clinics in your city.
You can hold out but what is your edge in this case where your competitor is now bigger and can handle things like a vet quitting as they have a bunch that roam from practice to practice. Or they can handle buying a new machine for millions while the bank won't lend to you due to your shrinking margins.
Economies of scale are a thing and can be a very real competitive differentiator.
You the hold out are now getting crushed by your competitors while you look around and see your fellow vets taking weekends off to take their new boat to the lake because they sold their practice and you're working your 11th weekend in a row because your other vet quit to work for your competitor that can now pay more than you.
I've had friends live this and its not fun.