I don't have a problem with someone asking occassionaly. That is certainly fine. Anyone could lose track of the count. The problem is when you give the count and they aren't paying attention and ask for it again. The problem is when you just said "3 balls, 1 strike" then call the next pitch "strike" and before you can take a breath you hear, "Hey, Blue, what's the count?" We are umpires, not score boards. Why don't coaches bug the score keeper for the count rather than asking the umpires all the time, quite possibly distracting them from other responsibilities?
Probably because we always know where the umpire is an often have no clue who or where the official scorer who may be from the other team is.
I think it is rare a coach will ask the count after a clear call and signal of the count but then I'm not behind home plate with coaches asking me.