Quoting Geordi La Forge: "The Enterprise-E is the most advanced ship in the fleet, we should be on the frontlines"
The producers decision to keep the Enterprise-E (and the Sovereign Class) solely for movie purposes was a major screw-up, considering they decided to have a 3+ year long story arc regarding the Dominion War. And the existence of the Enterprise-E is known BEFORE the outbreak of the war. We should've seen the Enterprise atleast once, or for that matter, mentioned quite a bit more.
The Sovereign and Defiant Classes are among the most advanced in the fleet, as well as the Prometheus Class. And yet, in most CGI scenes we end up seeing Excelsior, Miranda and Galaxy Classes being blown up left and right. Budget purposes ofcourse.