Great points. I wouldn't want to live in a world without the Beatles!

The band most famous for being influential without having been famous would probably be the Velvet Underground. (Eno is often quoted as having said "The first Velvet Underground album only sold 10,000 copies, but everyone who bought it formed a band.") Removing the Velvet Underground from the mix would truly be disastrous. But practically no one today knows their original works.