Part of the answer to this question is, it's an inexpensive "best practice" thing to do that might cut hum & noise by a coupla percent. After all; if I am dependent upon the steel of the chassis (steel: not the best of conductors, but OTOH, there is a lot of it) then that chassis subject to all manner of currents running around in it, in quite the unpredictable basis. Those pots are in and/or before the high gain part of an amp. You would really, really like for them not to be a problem, I suspect.
If you look at the traditional and most (by far) widely used flavor of control, CTS; or, if you have ever taken one apart, you will see that the enclosure ("can") of the pot is held onto the front (where the threaded bushing which goes thru the chassis and is hopefully star-washer mounted) by four fold-over tabs. Undoubtedly, those are folded over by machine which stomps on them pretty well during manufacture and probably makes an excellent connection to the bushing part of the pot.
Until you move to Los Angeles and get a little bit of smog in the air, maybe. Fast forward several years. Hot > cold > hot > cold > hot > cold, inside an amplifier. Vibration. Chemical reaction/corrosion possible. Throwing that ground wire across the back is just an OCD way of ensuring that the grounding scheme that existed the minute your last solder joint firmed up persists on a permanent basis, and you are sure of it. >>IF<< it turned out that this was a necessary thing for you to do to reduce hum; it's maybe 5x easier to it while you're doing the build than afterwards.