Yeah, the Enterprise-A was unique. It was a PR exercise, basically Starfleet throwing all their rotten eggs in one basket where they could keep an eye on them. Sulu got time off for good behaviour.
The only two missions we see reflect this. They are sent to Paradise City specifically because Admiral Bob thinks Kirk will cause the Klingons to "think twice". In reality it does the exact opposite. He's sent to escort Gorkon because his hatred of Klingons is well-known and will make him the perfect fall-guy in the conspiracy. It's clear that Cartwright pushed behind the scenes, and perhaps influenced Spock to 'volunteer' the ship.
Hmm. I guess that's one way to look at it, LOL.
