Interestingly, we saw lot of Galaxy-class starships on DS9.
Most of them appeared after the Enterprise-D had been destroyed. Notable exceptions are the Enterprise-D in the pilot and the Odyssey in season 2.
However, people who don't know (occasional viewers?) that Captain Kirk isn't supposed to show in the first season of TNG, might also don't know that the Enterprise-D is already destroyed in the timeframe of, let's say, DS9's 6th season.
I don't think that its unlikely that a occasional viewer sees a Galaxy-class starship in a Dominion War battle scene and says: "Hey, that's the Enterprise!" And as far as I understand it, that's the whole point why a Constitution-class starship didn't show up on TNG.