Out of universe, the reason why there are very few Vulcan stories in Star Trek TNG (and to a lesser extent DS9 and Voyager) is that Gene Roddenberry explicitly barred potential writers from writing stories about them:
"No stories about warfare with Klingons or Romulans, and no stories
with Vulcans. We are determined not to copy ourselves and believe
there must be other interesting aliens in a galaxy filled with
billions of stars and planets" - Star Trek: The Next Generation Writer/Director's Guide
Ultimately, there was a conscious effort on the part of the studio to make shows that were at once similar to the old TOS show (notably the look and feel of the tech and the camaraderie of the crew) but also dramatically different (by introducing new aliens and situations).
It wasn't until after Roddenberry's death that a number of sacred cows seem to have been dispensed with, notably the prohibition on writing episodes based around the earlier crew and episodes containing Vulcans.