The Enterprise is the Flagship, isn't it? Who's to say that Admiral Pike doesn't have an office onboard the ship to keep an eye on everything while Kirk captains the ship? That is how it's done on a flagship, isn't it?
Actually a good point, flag ships generally have flag officers on board, so the Enterprise in previous incarnations is an oddity here (though I'd say most captains would defer to the flag captain in any instance where multiple ships are on the scene). Aren't ship operations aboard flagships left to the flag captain, while the admiral concentrates his mind/efforts on running and commanding the fleet in any endevour and just uses the ship to fly his flag?