First, opening a clinic requires some serious money. Then, if the new clinic gets traction, PE can make a very good offer for a buyout and the owner would have to be stupid or very stubborn to refuse. Most big companies these days just buy up competition. Good for the owners but bad for the customers.
Another thing which I've seen personally is that in general getting from 0 to 1 required HEROIC effort to the point that it requires a personality type.
How many veterinarians got into the game to become relentless, driven, scrappy and indomitable business owners vs because they love furry things and helping?