In ST2, it's quite explicit that a Quadrant is smaller than a Sector: it was unusual for the
Reliant to pop up unannounced in the same Sector as the
Enterprise, but even more unusual for it to also be in the same Quadrant:
Sulu (with steadily growing amazement in voice): "Reliant in our Sector (or perhaps Section?), this Quadrant, Sir... and slowing."
In TOS, Quadrant also was always a very small segment of space, a means of establishing the location at the accuracy of about one solar system (when a 20lyx20lyx20ly sector could theoretically contain a dozen).
That in mind, Kirk's ship was "the only one in the quadrant" only thrice: "Journey to Babel", "How Sharper Than a Serpent's Tooth" and ST2. In the first one, this was probably by deliberate design: other ships were kept away from the route of the important VIP mission. In the second one, Kirk was clearly going where no man had gone before, so no problem if it wasn't rush hour. In the third one, Kirk was letting Sulu "indulge himself", so they were probably wandering off the beaten path, and Regula I would be away from the rest of Starfleet by design, too.
So, being the only ship in the quadrant should be welcome continuity rather than an annoying contradiction in those episodes and movies.
Let's stop worrying about quadrants, then; they're not relevant to the discussion at hand. Which is, why was Kirk's ship the only one near Earth in TMP and ST:GEN? Those are the only two occasions in Trek history when this happened, to be sure. It happened to Archer once as well, but back then Starfleet was supposedly really small. It never happened to Picard or Sisko or Janeway.
We don't need sweeping explanations. We only need special explanations for two movies.
Timo Saloniemi