I coach and referee and junior level, and anything with RoRo subs it seems pretty pointless to ask the player to leave the FOP.
I won;t allow coaches to enter without a signal from me, which is usually given at the time I blow to stop play. I am a little more quick to stop play with kids than seniors though.
A couple of seconds to make sure no bones broken and no blood being spilled, and he is either taken off, or left on - that is up to coach.
Usually, and depending on age, coach runs on, picks kid up, runs off shouting 'Jimmy, Jimmy! Get your jacket off and get in midfield!"
Never have I been criticised for allowing too long with an injured child.