I get the impression that Starfleet used them more like galactic troubleshooters rather than have them on general duties. After then-Admiral Kirk's criminal acts, they'd keep him on a tight leash. It feels like it was only a PR stunt to keep him around, because after saving the Earth, they couldn't exactly lock him in a stockade. It certainly seems that by the events of TUC, they've been kicking around Earth for quite a while. Spock's been off negotiating with the Klingons, Scotty's all set to retire, Uhura's moving into academia... an early draft had Kirk reassembling his retired crew for one last mission, and that's a feeling that endures into the final film, even if it's not explicitly stated.
The "gaseous anomaly" survey might be a red herring; all Uhura says is that they are carrying the equipment, not that they've necessarily used it of late. I like Timo's suggestion that it's a euphemistic cover story for the Excelsior's real mission. Sending their newest battlecruiser on a three-year survey mission seems an odd use of resources.
TUC is a bit nebulous as to whether the ship is being decommissioned, or if it's Kirk and his senior staff who are stepping down from active shipboard service. The damage didn't seem to be too severe, so if it's a newish ship, maybe she's going to be patched up and renamed, as some think she was in the first place? I prefer the idea that the Enterprise-A was an old, refurbished ship, which happened to be surplus when Kirk and company needed a new vessel.
On the other hand, maybe it's the whole Constitution line which is being scrapped, per the Khitomer Accords? Ditching a load of ageing, unwieldy battleships in favour of the newer Excelsior-class probably makes sense. We never see Constitutions after TUC, with the exception of the wrecked hull in the BoBW graveyard. Maybe they were mothballed, as the admiral in the briefing predicted?
I'd love to read Greg's book to find out his take, should he ever write it!