Hmmm, not sure I buy your rationale, but we can disagree.
Incidentally, the CCA Mens Crew of Three manual does not specify a procedure for bringing in subs, except to say that the crew should ensure that the ball is not about to be put im play, and that the subs have reported to the table before entering.
You do it your way, I'll do it mine....in the end, the really important thing is to pregame it and be on the same page!
You say to-may-to, I say to-mah-to....