It seems to have more to do with the fact that tenors have the loudest/fullest sound of the three standard sizes. Obviously there's variation instrument to instrument, but there's a combination of factors that make tenors a common choice for professional musicians: volume, depth/richness of tone, fret spacing, versatility... Like others have said, it depends on your goals. What sound do you prefer? What style of music do you play? And so on.
I don't think it's because tenors have the "loudest/fullest sound" - the baritone, because of its larger body, can easily put out a louder sound (like comparing different sized speakers). There's also the conception of loudness (that is covered in the "Mya-Moe Loudness?" thread and Gordon's video about it), but that's a different story.
I think it's a mixture of things, from "the cool boys play it" to the common size that fits our tastes/feels. I can play soprano, concert, tenor, baritone, guilele, but I feel most at home with the tenor because the feel is right to me, and it's (in a sense) easier to play than all the others for a majority of styles. Also, I think the baritone has been shunned since its inception by most people (being the odd one out that isn't GCEA standard), which is probably why it hasn't gotten much appeal compared to the tenor - also, because many people think of it more as a "mini guitar" than an ukulele with the deeper sound. I remember one member on this forum who called the baritone the "bastard child of the 'uke family" - that remark made me chuckle a bit.
Technically, we're all playing "mini guitars." The ukulele is a cousin of the guitar, and both are descended from the lute. The guitar, in case no one knows, used to be four strings. Ever wonder why the notes are EADGBE? DGBE makes sense, because the intervals are 4th-3rd-4th. But the guitar is 4th-4th-4th-3rd-4th. I didn't really think about it until I came across it in my studies, but the extra bass strings (the last two strings, E & A) were added in individually over time. Basically, we had a 4-string and 5-string guitar before the 6-string.
Now why does this matter? Because the low G tenor is reminiscent of the first 4-string guitar (I think the first guitars were approximately modern-tenor size). The guitar, however, began to metamorph over time, growing bigger with each passing model and adding strings until we have our common 6-string today. The ukulele is special in that (as Dirk will also point out) the ukulele is still undergoing something like "birthing pains." I believe there's still more progress to be made in the ukulele world - the violin family didn't stop with one tuning, why should we?
Anyways, when it comes down to it, it's always personal preference. And I think it's pretty good coincidence that many choose the tenor.
(Hmm... I think I may have taken a long detour to respond haha)