No. Some pets do have dietary restrictions. This dietary restriction can be permanent or momentary, but they do exist.

My youngest (in age, and also the last in being adopted) cat, who had lived three years on the streets until she appeared at our doorstep, came not having eating well (or at all) for who knows how much time (she was malnourished) to the point that she couldn’t tolerate the food my oldest cats ate, so she was prescribed special food for her, so she’d have an easy time adjusting herself to eat everyday ones again (or for the first time, as we don’t know if she ever had a home before, or if she was born in the streets). Now, three years later, she’s doing great and fully eating common cat food (which she began to do last year).

But, vets always have brands that they advertise for. The brand ours advertise is too expensive, so we went/go another route for both the common food and the dietary restriction food. Luckily a friend of my mum has a pet shop so she could get us the cheaper, but equal in content and quality, food brand for us.

So it sort of means what you mean by “prescription” pet food. There are pets that definitely cannot eat “standard” formulations of pet food. Overweight pets are a good example of this: they need less calories, but you can’t just reduce the portion size without them feeling hungry all the time, which is just cruel because you can’t explain to them why they need to eat less. So a specialised weight loss pet food allows you to give them the same quantity of food, but it has less calories in it. For cats (I’m less familiar with dog food) there’s formulations for kidney function, for odour reduction (dear god, the smells that come out of one of mine would melt the paint off the walls without this food!), and so on.

Vets will definitely try to sell you these as “prescriptions”, and they sell them at a massive markup. But a lot of the time, these special foods are available from wholesalers and direct from the brand’s website at a much, much lower price. So my recommendation is that if a vet recommends a certain prescription food to deal with a specific medical issue, don’t buy it from them, because chances are you can get either the same food or something substantially similar from another source.

No. My kitty is like me in that he is prone to kidney stones (or for him they call them crystals”.

I give him prescription urinary tract food and it 100% makes a difference.

There are also many animals with specific diet or allergy requirements

I don’t think so, at least not usually. If anything, regular dry pet food is closer to a scam, especially cat food - wet food is just a lot better for them.

Regular (especially dry) petfood also uses a lot of meats and plants that a cat would normally never eat in their regular diet. And this meat is usually the cheapest, least desirable scraps from farms, because pet food isn’t usually subject to the same safety and testing regulations as human food.

Meat based on fish can contain contaminants from ocean pollution (like mercury) that accumulates in the food chain and (I speculate) might be a bigger concern for some pets than others, like if they have kidney problems that make it harder to filter out toxins.

Prescription pet food can be used to address a vitamin deficiency, to avoid an ingredient the cat can’t digest, to add more fiber to help with digestion, to avoid an allergen, or so on, just like a human diet.

The vet should tell you why it’s prescribed in a particular case, though, especially if you ask. If they can’t then maybe I’d be doubtful, personally.

Edit: if in doubt, get a 2nd opinion from another vet, like you would with human doctors.