I occasionally wonder if they have ever thought about the fact that if cows and chickens weren't tasty, they would likely be extinct?
Probably. Either that, or they would evolve into more capable species through survival of the fittest. Those species, as well as other ones we grow only for their meat, eggs, milk and fur, were never widely spread in the wild to begin with - we created them through selective breeding.
Another question is, would it be a tragedy if they went extinct?
We've taken over massive wildlife areas to feed them and and keep them protected and confined, and in doing so, we have brought varying degrees of danger to some wild species, from displacement to total extinction. Factor in the miserable living conditions of many of those animals (not all of them, I know - I don't mean cows peacefully grazing on prairies, I mean chickens living in the dark, fed processed food and pumped full of hormones so they can lay more eggs / be delivered as food as quickly as possible), and the question becomes less easy.
Full disclosure, this is by no means a defense of PETA. I don't know enough about them to have a strong opinion, but those "defamation" accusations they are making and other stuff in the HuffPost article don't exactly portray them in a positive light in my book.