When a runner misses a base, or leaves base on a caught ball before it is first touched, and the play ends without the runner returning to retouch the base, or without the fielding team putting the runner out, should the fielding team "appeal" the play by holding the ball at the missed or vacated base once the play is concluded?

No. After the play has concluded, any Ref that witnessed a runner miss a base or leave one prematurely may call the runner out at that time, without the formality of appeal (see Rules 10.05, 14.02f, l, and m). Any Out so called is applied as of the end of the play.

Note that any runner leaving a base before a pitched ball is kicked is immediately out (see Rules 10.03 and 14.02g).