Early arrangers really only had the two variations and a fill up/fill down, so a simple footswitch could toggle between the two. Nowadays, with four variations and six or so fills, a simple toggle is insufficient.

While some people eschew pedals, I think for the person that is actually PLAYING a lot, rather than 'operating' the arranger, having at least Variation selection (with AutoFill ON) at your feet removes most of the player having to take his hands off the keyboard (and consequently, stop playing) during the song, especially for songs with a lot of changes. I use the Roland seven switch pedal, and other than intros and endings, can go through many songs without needing to push the panel buttons at all except for tone or registration changes.

Timing always seems to suffer when you have to dash back and forth to the buttons. Fills and turnarounds especially always seem to have more changes than many verses or choruses, but that is precisely the time when you DO have to go hit buttons.

Organists seem to have no problem playing from between 13 to 27 'switches' at their feet well enough to actually play a melody (or bass line!), and yet some consider that even ONE pedal is too much... I just don't think they are trying hard enough

Probably the one operation you do more than any other while you play is trigger the variation changes (you ARE using them as much as possible, aren't you?!). Shifting this ONE thing to your feet allows you to concentrate on the playing, and less on stabbing at buttons and dashing madly back to the keyboard (where you usually make a clam in your haste)...