This is more like a modern Mt. Rushmore. I don't think Axl belongs in there though. And as cartoonish as Motley Crue is, I put Tommy Lee over Lars. Obviously some better drummers out there but I don't know that Neal Peart was particularly influential. For maybe the same reason as Mercury below.
Imo, Mt. Rushmore should be farther back than this group. People that were innovators or had strong influence of later styles. It's why I'm not sure that Freddie Mercury belongs on it. Talent wise, he'd be on there. But as good as he was, and as much as other vocalists respected him, I don't think he was a huge influence on future singers. I can only think of a few that even tried to sing in that style. It's just too difficult.
I think the easiest pick for the Mt. Rushmore is Hendrix.
For the drummer, I think a strong case could be made for John Bonham.
Vocalist becomes difficult. I think Plant seems near the top but I didn't really want to include multiple members from the same band.
Bassist, I really don't know. Maybe John Enwistle.
I don't think the Mt. Rushmore should extend back to Chuck Berry or those guys because even though there may be commone elements, the sound of what they were doing is way different from current day. While you can still easily pick out Zeppelin riffs.