My dog HAD to be vegetarian. She was allergic to everything, including animal proteins. She had special vet vegetarian food she ate all of her (1 day short of) 12 years of allergy hell.
She did well besides the allergies and hip dysplasia. But, the vet diets probably ensure certain supplements are included.
That’s a pretty unnatural diet. Most dog people think a raw diet cures allergies (and that the allergies are more about what else is in the dog food). I’ve tried feeding raw in the short term and all I can say is that it was fabulous. If I couldn’t get a premixed meat, I’m not sure I would have kept feeding it.