Yes if they have allergies you get what they need to keep them healthy no matter what. No argument there. If my dog needed to live on nothing but Kobe beef I'd do it. But there is so much marketing out there that suggests ALL dogs need specialty food and that's not true.

I won't do any work on my own birds so I have a veterinarian for my parrots. I switched because the one kept insisting I had to feed the expensive food his clinic sold. My new bird vet gave me a list of good foods and said feed a mixture because birds are picky and if they are used to a single food and suddenly you can't get it they may refuse to eat at all and get very sick. That advice made more sense.
Though I'm convinced my African Grey only uses his parrot food for target practice and survives solely on the human food he can steal when he is out of his cage. He is flighted so he is tricky. I should get a video because if you are eating a banana he will dive bomb you, impale the banana on his beak and fly away with as much as he can get...