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.