The Constitution Class Enterprise (i.e. NCC-1701-A) had the trademark of being "Kirk's ship", thus it's appearance in TNG at a time when we still had movies with the original Crew would have confused general audiences.
I call BS on this explanation. TNG had quite a few episodes depicting the Excelsior class ships, and no one was confused thinking that was either Stiles' ship or later, Sulu's ship. The audience would have been bright enough to figure out that a Constitution class doesn't necessarily mean Kirk's Enterprise. And when they finally did show a Constitution, named Defiant BTW, no one confused it with being either Kirk's Enterprise, or Sisko's Defiant.
I think the real reason was probably just a political pissing contest and over royalties between Paramount not wanting to grant ILM or CBS a model or CGI template of a refit constitution class ship, when the TOS cst were making movies at the same time as TNG was in first run.