The SF EX games lacked the pacing, fluidity and timing of the 2D Street Fighter games the base liked at the time, plus in terms of 3D it wasn't as impressive as its competitors (though I was awed seeing it as a kid in arcades).
Street Fighter III gutted all of the favorites from SF2 outside of Ken and Ryu (and originally they weren't even planned to be included), and didn't seem as flashy as the Vs. games. It was also HORRIBLY balanced, to the point it was a disaster for competitive play. Also I feel that the parry mechanic may've been a bit too punishing for some players to adjust to. Lastly, the CPSIII system was very expensive for Capcom to produce; it got so bad that they were super-quick to abandon CPS3 and move on to Sega's NAOMI board.
The quick shift in arcade boards for them IMO also impacted the development of Third Strike; it may be loved by a lot of the FGC today but I think that's due to a combination of having gotten used to its quirks and memories from stuff like Evo Moment #37; actually playing the game regularly these days if one's nostalgia glasses aren't on too tight, they can still notice lots of questionable imbalances and certain sprites (like Hugo's) weren't even finished, and background quality/detail was actually downgraded from Second Impact. It's still a great game but IMO it's not the godly savior of fighting games some of the hardcore fans (and internet casuals who barely have played the game extensively) try making it out to be.
Even so, elements from both the EX games and SFIII series have helped shape Street Fighter into what it is today, so they still deserve their props and respect for that.
Because
1) It didn’t really take off with fans until 3rd strike
2) Arcades were dying
3) For whatever idiotic reason it was a Dreamcast exclusive. Completely bypassing PS1 and N64 and only getting to PS2 in 2004 (5 years later)
SFIII on PS1 would've likely ran like dogshit; it was already somewhat starved for VRAM which was essential for 2D fighters at the time, but the CPU was likely also a bottleneck in a port of the game to that system. Keep in mind; the sprites could've technically been transformed into flat polygons for rendering on PS1 to get around that system's lack of dedicated sprite hardware (and this is how modern GPUs basically render sprites; they're flat polygons or clusters of flat polygons with warping and other effects handled through the GPU). However, the 3D in home consoles at that time wasn't capable enough to completely convert 2D sprite games in this fashion, and the amount of VRAM at that time DEFINITELY wasn't enough to completely offset lack of dedicated sprite hardware in a system for 2D games.
A port of SFIII being dogshit for that gen arguably can also be said of Saturn, though they had the option of 4MB RAM Cartridge if they wanted. Still likely wouldn't of helped in a port all that much as, again, the CPU(s in Saturn's case) would've been a limiting factor.
N64 simply
could not get a port of the game. Granted, at the time it was a miracle it got a port of RE2 and Angel Studios did really well in compressing the FMV, but doing that same thing with sprites used in actual gameplay would've been a MUCH different deal and likely degraded their quality beyond recognition, that's even considering the largest N64 cart at the time. Also the N64 lacked a dedicated sound processor, so the music would've either been completed scaled back or sound different reprogrammed as MIDI or something.
Those are the reasons why the earliest SFIII ports were to Dreamcast; it was the first home console that could actually do virtually arcade-perfect port of those games without much to any compromises (I know the games have slightly different frame timing in the Dreamcast ports that some purists dislike, but visual fidelity-wise it's 1:1 with the arcade versions something that would've never came close to happening on PS1, Saturn or especially N64).