For the sake of control, there is some information every GM in his right mind keeps to himself during a fight. This includes hidden traps and secret doors in the combat area and probably most of the information regarding NPCs that is not visible to the PCs.
I can only speak for myself, but at some point the need for control conflicts with the need for free headspace. Though I dare say that all save the idiot savant get at least slightly dizzy after a long night of calculations, keeping track of NPC agendas, tactics and movement, consulting the attack & critical tables, looking up rules and definitions, etc.
For many the solution is to give up some control. For instance, I imagine most GM think it's fine to let the players know exactly how many hits their opponents has taken at any given point during the fight, instead of saying "he looks pretty messed up, limping and bleeding from his right arm". This allows for delegating the task of tracking the damage inflicted on PCs and NPCs, which again give the GM an opportunity to allocate his mental resources elsewhere.
I imagine that different GMs solve this problem in various ways, according to their own strengths and weaknesses. Many may not see this as a problem at all. Me, I'm quite happy outsourcing some tasks to my players (owing to limited headspace, no doubt). That said I do of course recognize the need for control, so while I outsource the keeping score of damages and let them do much of the calculation, I am for instance the one in control of looking up and reading out loud attack results and critical results, owing to the players not knowing their NPCs OBs, DBs, etc.
Different GMs draw the line differently, meaning the tasks done by players and GMs vary in different groups. Are you a control freak GM or more of a lazy/limited working memory GM? What do you let your players know and what do you consider absolutley secret information? And what are the consequences of this? Which tasks do you reckon the players can be "trusted with" during a fight? Ever heard of GMs giving up almost all control, save the most obvious such as hidden traps?