I would say the reason we never hear about a Captain's Yacht on TNG has more to do with Chekhov's Gun than it does with a Yacht not existing. There was never a plot reason to discuss the Yacht, so it was never brought up. We finally see a Yacht in
ST: Insurrection, which means it existed in
First Contact and in
Nemesis, but likewise was never brought up. It would be too complicated to try and implicate that the Yacht was added to the Ent-E prior to the events of Insurrection, and then silently removed afterwards.