Good points. As I watched the installation demonstration, my first thought was that one should never remove the nut from a potentiometer without opening the case so that the body of the pot can be grasped while applying pressure to the nut. (The exception is pots that have a registration pin, but you don't normally see those on stompboxes.)
Not doing so risks internal damage. Twisting the pot can break the wires connected to it if they don't have enough slack in them. Some pots are soldered to circuit boards, and twisting them can break solder connections or even lift traces from the printed circuit. Some pots are cheaply constructed, made almost entirely of plastic, and are therefore fragile. These problems can occur either while loosening or tightening the nut.
As for the different shaft styles, those aren't
necessarily a problem. I have replaced knobs many times using generic knobs on technically-incompatible split, splined and keyed shafts, and usually they work acceptably well. Sometimes you have to slightly rotate the knob so that the set screw doesn't go into the split or so it lines up with the flat part if the shaft has one.
I have, however, broken split shafts doing this, so the practice is not entirely without peril.