bartenders... any theory behind customers leaving some of their draft beer behind when they go?

It’s a small sacrifice of thanks to the beer Gods.

Ninkasi thanks you, as does the kid I tutor in my spare time.

Have you never seen people leave food on their plate? My counter question to your OP is, “why is there anything weird or confusing about leaving unfinished alcohol as opposed to any other unfinished consumable?”

Yup, and it’s probably half spit by then too. Yeuch.

It’s so when they get home and their wives ask “did you stop at the bar on the way home and drink a beer?” they can tell them “no, dear, I did not.”