Random thoughts and opinions:
Funny, I have never gotten on with tenor as a player, even though I have probably earned more money on tenor than any other. My true voice is either alto or baritone. Tenor and soprano, not so much. Just starting to play bass sax, it'll be interesting to see how that develops.
I think tenor preference is mostly about rock and roll experience.
Alto in rock and roll sounds too light to me, almost childish (as distinct from funk type stuff where it has a place, but often with a horn section in the mix too). Baritone in rock and roll sounds great, but once you get in the upper register to project you start getting that strained sound. Bright high baffle MPs on bari just make it sound like a kazoo, and a setup that makes it sound like a sax doesn't project. Bright high baffle MPs on tenor sound great, because the frequencies are higher so you don't get the kazoo effect. Tenor is low enough to sound strong, but high enough to project.
In jazz I think it's Hawkins/Young/Coltrane that drove the generations of tenor players. Of course there have been generations of great alto players all through too.
Another thing to think about is that big bands from the 50s through the 80s got progressively louder and more rock and roll like. So again the sax players start looking for projection. I think it's easier to project over a big band when soloing with a tenor with a bright setup, whereas with an alto you can project but it starts to sound strained and shrill. Furthermore, the trumpets have been getting darker and darker (nowadays, a brass player who played a horn like the greats of the 30s and 40s would be derided for playing a "peashooter"), thus starting to move into the sax space, particularly the alto, whereas tenor is kind of in between the trombones and trumpets. Why are big bands important? Because in this day and age, school big bands are where most young people get their first exposure to jazz - heck, the first exposure to playing non classical music on wind instruments. So if all the big band charts have the most meaty solos in tenor, because of range and timbre matters, then young students will feel that tenor is the horn for jazz soloing (which bleeds over into rock and roll) and alto is the horn for precisely playing lead and inner parts. (And they think baritone is the horn for the worst player in the section - AAUUGH!! - wrong, wrong, wrong - but that's a whole other discussion.)