Is it common to feed cats only 1 brand/flavor of canned/dry food for their live?

It's hard to know for sure, because it seems unlikely anyone's taken a formal survey on the subject, but I suspect that while some owners certainly do give their cats variety, that a reasonably large percentage really do feed their cat the same food unless they are forced to change it, usually to address a new health problem.

The reason why I think this is due to some common cat personality types or particular needs. Many cats actually hate or become stressed at any sort of change, while other cats are just very picky, and so it's a struggle to find them a food they'll actually eat in the first place. There are also many cats that have intolerances to certain foods, that will make them vomit, have diarrhea, or have excessive flatulence, and so forth. So again, owners with these cats will surely stick to the one food they discover that the cat can eat without experiencing these sorts of symptoms.