I'd say it has to do with the Mini/Toad dungeons as well as things like Garuda and the Cave of Darkness which even with the rebalance in IIIDS, are significantly less frustrating when you bother to bring the right class. The game structure around having the right classes to solve the issue at hand doesn't lend itself well to speed runs.

I will also concur that the game's lack of awareness within the FF community is also an issue as at least FFV has been a well known cult classic since the 90s whereas III was "that game on the NES that did the job class system first, but forget it, because FFV did it better."