I guess I can find a scenario where a player won't make a significant impact in the first 20 games, but is valuable over the course of the season, and future seasons. You do not. You're rolling the dice somewhat, maybe, where if you miss the playoffs by a game, you'll wonder if said player would have helped you. It's a risk/reward thing.
An example:
whatifsports.com/HBD/Pages/Popups/PlayerProfile.aspx
I actually didn't wait to call up the player below. When he asked for 3.8M this year, I tried to trade him, couldn't and then cut him before his 3rd arb. He got 1.3M his first year of arb. He got 2.4M his 2nd year of arb. Would I have preferred to give him the minimum salary 2 years ago and 1.1M less last year? Of course. Maybe I spend that money in a way that helps me in those 2 last seasons. And I don't think it would have done much damage to me in that first season if I held him back because the difference between my team and the competing team in my division was 16 games. I would argue that in hindsight, I should have held him back. That's my point, that there's a risk/reward you have to look at, and it may make some sense to hold back in some situations.