One more example of a band with no stable lineup is the very prolific Guided by Voices. It’s understood the “band” is really just Robert Pollard and whoever he chooses to surround himself with at the time. But even if he writes all the songs, he still fleshes them out into band arrangements with other people, and it’s definitely rock band music (apart from his occasional solo numbers). I think his touring lineup has been a bit more stable but in general, good luck forming any coherent concept of “core membership” for that band beyond Pollard.
BUT, nobody ever argues with the branding. Nobody’s saying, “Is that really a GBV album?” Which gets back to my earlier point, that an artist gets to define themself. They don’t need our input.