In high school, JV, and JH games, it is customary to count the players after coming out of EVERY timeout. Mainly to ensure there are no more than 5 players on the court, which happens most frequently. It isn't done to "help" the coaches but to ensure there are only 5 players on each team. If an officiating crew counts each team and notices one of them only has 4 players on the court, it is customary to inform the coach. The official(s) not inbounding the ball (either in a 2-person or 3-person crew) should signal to the referee inbounding the ball that they are ready for play. If the college-level officials don't do that, it seems like a failure to properly manage the game.
End result is that it is still the head coach's responsibility, but proper/fair game management by the officials also comes into play. Especially at the most critical juncture for end-of-game situations.