Influence - what bands cite the Stones as a big influence ? I’ll wait.
Beatles - several, Zeppelin - Black Sabbath, Pink Floyd. and even KISS can cite several 90s era grunge bands and a few others inspired by the bands/era. None as good obviously - but Nirvana is still a pretty damn good one to cite you as an influence.
Point is - just as many say Zeppelin just popularized what a bunch of blues musicians did to white kids - Stones did the same. They created their own twist - but yea - they took more than they put back out as an influence. Still made alot of memorable songs over a 20 year stretch. But name me a stones song the average person will know POST 1995.