The model of PE in dentistry / veterinary clinics is to buy out all the private clinics in a region, then gradually raise prices. Small businesses would pop up, but the training horizon for new dentists / vets is quite long.

It isn't really about economies of scale so much as using local monopolies to set prices. They have a good moat because regulatory bodies have not regulated monopolies for 30 years, and professional organizations limit entry to each field.