Anecdotal
What I can give you is first hand, though anecdotal evidence, that yes, the more pressure, the cleaner powder burns.
It is no sectret that I, and many other Competitive Shooters, shoot in what we call "the upper load window". I have no idea what pressure level we shoot at, but plug a 68 grn bullet out of a 6PPC at 3450, and you can get an idea.
This results in a very clean barrel, even after enough rounds to shoot an Unlimited 10-Shot match. When I come from the line after a group, all of the 'black" is out of the barrel by the 3d patch.
I also believe it cuts down on carbon and copper fouling. In all honesty, I never pay any attention to either, my barrels just seem to stay foul free. They also shoot quite well.
I doubt it is because I am lucky. I do believe that the high pressures burn just about anything, and everything, in that barrel. I know shooters who use 133 down in the mid and lower load window, and they spend quite a bit of time getting all of the junk out of the barrel......jackie