It depends how tiny you make each pigeon-hole.
In the 'old days' you were either pop, rock, dance, jazz etc. It didn't really differentiate much finer than that.
The we got heavy rock, then heavy metal… punk got in the way for a while, but behind it disco & soul took their own route. Punk became new wave; then came electronic, which spawned another newspaper headline of new romantic…
..wind on another 30 years & we now so finely differentiate genres [e.g. garage; which sprung from house & has since spawned speed, 2-step, future & rock offspring in the UK alone] that some artists can struggle to stay inside the pigeon-hole their audience have forced them into.
Others fare better by having managed to stay out of a specific pigeon-hole altogether. Those seem to be the most long-lived.
Taking an example - U2 [doesn't matter whether you like them or not].
They have managed to continue to do pretty much the same thing for so long that they've ended up being in a pigeon-hole all of their own. "It sounds like U2" is about as close as you can get to forcing them into one. They're not really rock, though that would describe them in the very broadest terms, but you can't quite squeeze them into any other simple category.
So… is "U2" a genre?
Nope - it's a band, but one with such a distinctive sound that band & genre sit in a pigeon-hole with only one act in it.
Is "The Rolling Stones" a genre?
No, by the same token as above, they have been lucky to escape being pigeon-holed so tightly. The same could be said of many long-lived artists, including The Beatles, David Bowie, Queen; even Oasis managed to out-live their early Brit Pop tag.
Is "speed garage" a genre?
Yes - but one so tiny that the pigeon-hole is crowded, with acts falling out of it all the time & new ones taking up the space they previously occupied.
Each time enough acts fall out of that hole, someone will think up a new name for the direction they took, once more locking them into a new, tiny, genre.