AskBeehaw

A quick google search tells me that:

Veterinarians must prescribe certain therapeutic diets because, depending on the disease being addressed, these foods may contain levels of nutrients below what is legally allowed to be sold for a healthy pet without that medical condition.

and

While some are not appropriate for long-term use, as they’re not 100% nutritionally balanced (some low fat or low protein foods fall into this category), all are safe for pets in the short term.

and

veterinarians believe they might be misused by owners, or worse, implemented in lieu of veterinary care. Neither of these things are good for pets.

HOWEVER, I also found:

(Prescription Diet® is a registered trademark of Hills® Pet Nutrition, Inc.®)

and

In the dog food world, the term Prescription Diet® describes an effective marketing agreement between a hundred-million dollar pet food manufacturer and the veterinarian community. This agreement allows for the sale of their foods through licensed veterinarians only. Veterinarians benefit because they can achieve a much higher mark-up on these foods than they would by offering foods widely available without a “prescription.” The pet food manufacturer, in return, gains credibility as a manufacturer of veterinarian-recommended food and uses that as an endorsement, if you will, for the rest of their products.

Add to the data that I've heard (from a vet, but that's not a source you can verify yourself, so take that how you will) Hills is often kind of like a D&D 5e warlock patron for veterinarians, in that they give out a lot of scholarships and grants to people going through vet school, and many vet schools' only nutrition-based course is taught by people on Hills's payroll.