Yes, that would have been fantastic. Instead, we see Starfleet fighting a war with the Dominion with fleets primarily composed of out-of-date ships. No wonder they almost lost.
All the newer designs kept getting assigned to the Seventh Fleet, where they continued to get destroyed off-screen...
Maybe it's the other way around... we saw those older ships more because they had better survivability. In TWoK, the Enterprise
traded weapons fire while unshielded, and generally came out OK until the Reliant
was finally overwhelmed at the end. Compare that to the Galaxy class, where if you happen to get a lucky shot on the starboard power coupling... boom!