To be fair I doubt there are a lot of knobs like this, and Cliff does model the log curves of the pots on the amps so most scenarios are probably covered in a one-to-one basis
Well, ENGLs have, if I remember correctly, contour, some mid boost (contour is also a mid boost of sorts), bright, ultra bright, M.L.P., vintage/classic, something else I don't remember.
Rectifiers have a bunch of controls on the back panel, those are important as well.
Orange amps have weird controls, I think also like contour, but not quite the same contour as ENGLs, and those are knobs, not buttons.
If you omit all this stuff and just leave BMT and Gain, I doubt it'll be easier for anyone to dial in a good sound.