The honest reason why the Sovereign and Intrepid Class ships were not seen in the battles (this is from the Companion and an interview with the producers that is available online, I just don't have the link anymore):
Paramount Pictures told them they weren't allowed to use them. Paramount had defined several ship designs as "Hero Ships" and they were reserved for use on the specific shows that they were designed for only. This started with Roddenberry in TNG's first season during the episode "The Battle". Originally the Stargazer was going to be a Constitution Class ship but, because there were fears people would confuse the ship with the then Enterprise-A, Roddenberry and Paramount nixed the idea to prevent confusion among the fans (and the Constellation Class was born). This is also why we never see a Constitution Class ship on TNG (other than as an unidentified broken hulk in BOBWP2) because there were fears that it would be assumed that it was the Enterprise.
When DS9 began the Dominion War storylines it came up about having the Enterprise and Intrepid Class ships in some background scenes, but the producers nixed the idea because of this rule under the impression that people would automatically assume that Picard & Co were present (in the case of a Sovereign) and wonder why they weren't leading the fight from the Federation Flagship. The same was true of Voyager and they were worried there would be confusion about how Voyager was there. I remember reading that the producers thought it was a big deal they got approval to use the Intrepid model for the Bellereophon in Season Seven.
As for why we never saw Ambassador Class, Constellation Class, Norway Class, and Oberth Class ships in the war: that was because of CGI issues. There was never a CGI model built for the Ambassador, Constellation, or the Oberth Class ships and the Norway's model was lost due to a computer crash. Because they didn't want to waste money they never built them. Remember too that there were no Nebula Class ships in early battles either because of money issues.
So there are the real world reasons. In character maybe they were just in different fleets.