That's why Page tried to make his Les Paul so much like his Tele
Frankly though, I kind of do the same thing. I wired my humbucker Zemaitis guitars with a high pass filter so I can make the humbuckers sound like singles when I need to. I got that idea from the PTB (Passive Treble Bass) cicuit that's in my G&L Legacy. And my Teye guitar has what's called a mood control that does the same thing. I think Page moved to the Les Paul because he preferred the way the his Paul could conjure up the heavy tones with his stage amps, and when he backed up the volumes, the PAFs could get into the Tele zone.