Some of the greatest bands to ever exists are bands I rarely listen to for that reason. Great songs but I listened to them so much over the decades I end up changing the station when they come on. Much of Boston, Zep, Floyd, Fleetwood Mac, Tom Petty, John Mellencamp, Doobies , Stones, Springsteen. Sometimes it depends on the location I'm at when I hear them.
Same for pretty much all those artists.
EXCEPT a few songs I could listen to every day and never get sick of:
Allman Brothers - Midnight Rider
ZZ Top - Any of their stanky, nasty, dirty blues tunes, e.g., Blue Jean Blues, Fool For Your Stockings, Ten Foot Pole, Jesus Just Left Chicago, pretty much all their good stuff pre- and post-Eliminator. Nobody plays the blues like the Reverend Willie G.
Bad Co. - Silver, Blue and Gold
We could make a whole other thread about songs you never get sick of hearing.