Hmmm... so one of Starfleet's finest officers--I think if you're one of twelve starship commanders that's obvious... just gets thrown aside for a wargame???
I think 5 of them, really. Kirk was thrown aside, the possible captain of the Lexington and the 3 captains of the other 3 ships as well, you don't call what they were doing part of their normal duties. This was a Major
commitment by the Federation. If there really were only 12 like Enterprise, then that's 41% of their fleet in one spot, yet Enterprise is usually "the only ship in the _______ (quadrant, sector, area)" That's big. The regular Enterprise crew is in security detention, not shore leave. Wesley was shocked when Spock knew so much in the transporter room.
Just think about the areas of Fed space underdefended, if the Klingons or Romulans were aware, there's a huge potential for loss of life.