No one uses their stick to tilt except poor little ol' me....
I have full respect for both other options, so i don't feel like defending the tiltstick, but as its lone representative i suppose i should. I've been using the tilt stick for months upon months, It is quite innate to my play style now.
Benefits:
All three tilts can be done more quickly with tiltsticking.
You might think that you don't need up tilt, but it is good to use. It is better for diagonals, and if you choose to use it rather than upsmash and miss you will often hit your target on the other side.
Ftilt has been discussed already
Dtilt becomes faster, and also helps you be less predictable. Usually if you plan on using a down tilt, you start tilting the stick down just a little, which might make you duck and give away your plans. But with tilt stick you can go into a Dtilt from the standing position straight away.
And you still have all those aerial attacks, plus Nair. There is no way that i know of to fast fall a Nair without using tilt stick. Nor is there a way i know of to give constant right movement input and suddenly do a nair... you usually have to mess with your character's momentum somehow to do the nair.
As for Proverbs' original gripes:
The accidental jabs may be annoying, but they completely go away in about, i dunno, four days of using it. after that you will never see them again. Except every once in a while when i feel smug, so i tilt in the opposite direction of forward to do jab.
The accidental jumping is a bit more serious, it never goes away completely. It happens less and less as you get used to it.. however, know that it is not random, it is your own fault. I read.... somewhere... that it occurs when your ftilts are going slightly upward, and when you are spamming uptilts. (or any combination thereof). Something about reading in upward direction and tap jump, i dunno.
But after i read this i noticed something, that i the jumping tended to happen when the enemy was above. During my Ftilts i would be "thinking" upwards you could say. So although you don't want it to jump, it always makes you jump when there is something up there to jump to, since sometimes the input was subconscious.... The honest truth, sometimes i'll be doing an ftilt when an enemy is slightly above, and instead I'll jump, and since i'm still doing ftilt, I do a heel kick. Once, it was a sweetspot. But once again, the accident jumps happen less and less with time. It happens less than once during every 4 stock match. (on average. no one smart off at that)
*********The major unmentioned benefit of tiltstick**********
Is sheik's tilts. If you play a dual Zelda, like me, you have to use whatever set up you did for Zelda for Sheik too. And sheik has a much stronger case for the tiltstick. Her uptilt has better range and about equal precedence as her slower up smash, so you use it all the time. And tilt stick makes those Ftilt, Ftilt, Ftilt, Utilt combos much easier. Sheik also can use his dtilt for breathing room..... But the main huge enormous thing is Sheik's Utilt and Ftilt. Those are so wonderful when they are faster.