end of game procedure

[Tru_in_Blu]

I'm looking for inputs to settle (or advise on) a debate.

NFHS varsity game. At the conclusion of the game, plate umpire returns game balls to home team and begins to leave looking for BU to join so they can leave together.

The base umpire goes to the plate area. The BU that stayed at the plate area believes that (both) umpires are supposed to stay there to oversee the players going through the handshakes.

Is staying at the plate to do this part of any sanction's end of game procedure? Is it required or even recommended? Softball, baseball, other sports?

Thanx.