If you want (what I think) is the real reason: TPTB probably felt that since the Constitution Class Enterprise was a "hero" ship, there can't be another ship on screen that looked like it, since it could cause some confusion among the audience.
But that's just my two cents worth.
I would try to argue that no one thought the audience would be confusing the ship on screen with a "hero" ship when they showed all kinds of Galaxy class ships on DS9, but then considering how often I heard people say "is that the Enterprise?"...