I think actually what is happening is they are not babying Hader and already viewing him as the 3rd, or maybe 4th right behind Hughes, go-to bullpen arm. The issue is that CC, like almost every manager, does not understand how to use a bullpen and solely determines when to use different pitchers based on the inning. Nothing else is taken into consideration. Since it was the 6th, there was a 0% CC would have used his "7th inning" guy, or "setup man" or certainly not "closer". Also, Hader does probably need some babying, he now has 9 appearances and only has 1 where he not walked at least one hitter, that is horrendous.