Why do baserunners go back to their base after every pitch and foul ball, even if nobody is covering that base?  It seems so automatic that I thought it was a rule, but I’ve never heard of such a thing, or understand why it’d be a rule.

It is a rule on foul balls. Rule 5.09(e) directs that after a foul ball that is not caught, “The umpire shall not put the ball in play until all runners have retouched their bases.”

Well done.  Thanks, ess eff.