This is dialog from The Immunity Syndrome.
: "Kirk here. Go ahead."
: "You will divert immediately to sector three nine J."
: " Sir, the Enterprise just completed an exhausting mission. We're on our way in for R and R. There must be another starship in that sector."
: "Negative. This is a rescue priority. We've lost all contact with solar system Gamma Seven-A, which the Intrepid was investigating. And we've just lost contact with the Intrepid. Report progress."
: "Order acknowledged. Kirk out. Mister Kyle, you heard the order. Set course for Gamma Seven-A, warp five. "
Starfleet Command requested that the Enterprise undertake a new mission. Kirk initially presents reasons why he thought the ship shouldn't be given the mission, but in the end he accepts the new assignment. It was somewhat similar with Picard and the war game assignment, Starfleet Command requested that the Enterprise engage in the war game, Picard had his own reasons not to, but in the end accepted the request of his superiors.
Picard did what he was told, as any officer (even one with reservations) in a military hierarchy would.
When Captain Kirk was requested to engage in war games in The Ultimate Computer, he reallly didn't have a lot of options in the matter. Neither did Picard. If Picard could have presented Starfleet Command a real reason (beyond a vague unrealistic philosophical belief) that his ship shouldn't engage in the war game, perhaps then the assignment would have been cancelled.
This is dialog from Journey's End.
: "I understand your moral objections, Captain. If you wish, I can find someone else to command the Enterprise for this mission."
: "That will not be necessary, Admiral."
Starfleet's request was that the Enterprise
engage in the war game ... not Picard. Unless there was a damned good reason not to, THE SHIP
was going to be in that war game, with or without Picard.