Perhaps... but then what was the trans-warp we saw in the later series (most notably Voyager
, as it was made clear that the Borg use trans-warp conduits to travel)?
I don't think they ever said anything about the Excelsior's trans-warp drive after TSFS, and I believe the Encyclopedia theorizes that it was just an experiment that ended in failure (which is perhaps not canon, but a reasonable assumption).
Your theory has merit, but the obvious real-world explanation is that the writers on TOS never really gave much thought to the actual speed of each warp factor or what the absolute limit was. They probably didn't foresee that a time would come when a bunch of nerds would obsessively pick apart such matters.
The TNG-and on writers apparently did, so they settled on a new warp scale that was clearly different from the old one and had Warp 10 as infinite speed.
Of course, that brings us back to the original question, which is why, in the fictional Trek universe, did Starfleet switch to this warp scale (or rather, switch back, since the TNG-era warp scale was used on Enterprise
)? Who knows? We may never get an answer, but then again, I didn't really expect to get an answer on the "Klingon forehead" issue either. Maybe it's as simple as Kirk and co. using a system that is akin to kilometers/hour while everyone else was using something akin to miles/hour (you know Kirk, the renegade -- he always has to be a little different...).