I propose Kurt Cobain. I feel that he meets the criteria in spades. Known, loved and emulated by millions. I don't feel it can be argued that we was quite the game changer.
My monument includes Van Halen, Hendrix, Page and Cobain
Others I considered are Townshend and Frusciante. Though how can you have Mt. RUSHmore without Lifeson? ![Tongue :P](https://www.dreamtheaterforums.org/boards/Smileys/default/tongue.gif)
Reading through all of this, Cobain was my first thought as well, especially given the criteria laid out in the OP.
Look, I've spent most of my guitar-playing years attempting to cram as many notes into a measure as possible—I long worshiped at the alter of JP and Co., so I fully get the instinctive scrunch-face that occurs whenever Cobain's name appears in a guitar-centric conversation.
That all said, I also have about two decades of teaching experience, and during that time, I have watched the guitar go the way of boxing. For those unfamiliar with the analogy, there was a time when professional boxing reigned supreme, and the NFL and NBA were fledgling outliers on the sports landscape. Obviously, boxing still exists, but it is the veritable definition of niche at this point, especially in the U.S.
The same can be said for guitar. Fortunately, there are still 13-year olds out there falling in love with guitar rock, but they are few and far between.
After all of these years, I remain amazed by the staying power of Nirvana's brief musical output. The future of guitar/rock/music in general isn't people my age, it's 13-year-olds, and to this day, Nirvana remains a near unanimous starting point for so many of this kids.
Maybe twice in all of my years of teaching, a kid has come in and asked me, "have you ever heard of Dream Theater?"
Nirvana, on the other hand, is still an ever-present mainstay in my teaching repertoire.
While this final point is necessarily part of the OP, I personally feel that the ability to inspire others would factor heavily into
my Mt. Rushmore. For that reason, Cobain would probably be up there.