It is simply personal preference what one likes the most in waves, a TT or a Mutant or a Waveboard, of course.
But, this topic is all about "Why a directional in waves", from the original poster, right ?
Many prefer the TT in waves because they are relatively new, or experienced riders that has reached a level where they cant/dont evolve more, or a bit frightened in the waves, so will choose the safe choice they know
Which is fully understandable
Others are so much into freestyle, that they use TT's in waves and dont really ride waves at all, which is also understandable
Then some like something in between, a Mutant t.ex.
But very few today, as most want both a TT and a Waveboard instead - so choosing depending on what they like to do on a given day and conditions.
If you have some wave spot where the fins will get ripped off by underwater rocks pretty fast, a TT also makes sense, as fins are less likely to break and easier to replace
One could say, that with a waveboard you have the perfect board for riding waves of any size and direction, and you can jump high too - but not do the same easy freestyle moves, nope.
With a TT you can ride more powered/bigger kite, thus maybe sqeeze slightly more height in jumps - or maybe not.
But definitely more hangtime, as the kite is bigger.
And easier for the less experienced to "manage".
And Rightguard - if you choose a small waveboard, you get exactly what you want - better in the waves, but still feeling "small" and agile in jumps
You have to feel it yourself - before you know what the difference is, between a TT/Mutant and a Waveboard, but you have got many good answers in this thread now.
The reality though, is for most riders, that eventhough they got waveboards and jump a lot in the start (first years), it will wear off and one will begin to focus on waveriding and tricks in the waves instead - as jumping high gets boring pretty quickly, COMPARED to riding waves on a waveboard.
And a few stay in the "jump" mode forever, on waveboards - but not as many as those who ditches jumping almost for good, or just as the "occasional" blast - as it is awesome to just boost max on a waveboard
Simply a fact that for most riders, jumping wears "off" after starting to waveride - and then many ride strapless also, as it does not matter if they dont jump anyway - or maybe want to jump strapless and challenge themeselves even more.
But because waveriding is so awesome and a good feel on a waveboard, its a good thing - our own choice as we can do what we want, jumping or not
Riding on a TT or a very TT like board, most never experience above, and wonder why so many ride waveboards instead
Just trying to sum things up, to the original posters question.