Screamin’ Jay Hawkins and Screamin’ Lord Sutch were there with shock rock theatrics before Alice Cooper but I’m ok with him in the Hall (Lord Sutch also had an open ear for musicians giving some like Nicky Hopkins and Noel Redding their start).
Let me add The Pretty Things to the overlooked list.
I’d put The Faces on par with The Small Faces for inclusion and on that basis then put them both behind The Pretty Things.