You can't dash again right away? I also remember reading somewhere that you can't jump immediately after pivot? Or am I just making all of this up.
You can do anything you want out of a pivot. Your character is just in a standing position, with no momentum. It's done in place of wavedashes to move short distances very quickly and safely and is essential if you want to maximize your speed.
The easiest way to pivot is to just flick the stick in the opposite direction. It has to be done during the initial dash, since a pivot is just a DD that is cut short before the animation of the dash in the opposite direction begins, which starts right after you turn around. Since it's known that turning around takes 1 frame, I believe the stick has to return to neutral after the side input in 1 frame. Just flick the stick, it's not hard.
What is hard is doing moves quickly enough out of the pivot for it to be worth it. To be worth it, the input needs to be performed faster than the recovery lag of a wavedash (7 frames? 10 frames? I forget). It should be no problem to do pivot smashes, pivot SH aerials, and jabs using the flick method.
But it's pivot ftilting that's more difficult. Perfectly spaced ftilts and the ability to dash and do them with precision instead of having to do a riskier wavedash into them would be quite useful, but it's hard to do a fast tilt right after you've flicked the stick.
The other method allows guarantees the fastest possible pivot ftilts and fsmashes, but it requires some precision. As you know, forward is both need to do either move and it's used to do the pivot. But, forward must be released in one frame or else the dash begins! So, A has to be pressed at some specific time during the turnaround, probably on that one frame I'm thinking.
Pivoting into dtilits, utilts, or B moves (like shine) would be really powerful if someone were to master it. But it's hard
I agree WD back is probably more useful anyway, but being able to empty pivot would be a nice addition to WD back for more space. WD back -> Empty pivot is like a uber DD. But most of the time you're moving like that it's for a grab or to respace before you shield an aerial anyway.
You can't do things immediately out of wavedashes, but you can with pivots. WDing back is always more dangerous since it was a vulnerability period at the beginning, which is equal to the recovery of when you air dodge and hit the ground before it finishes (of course). However, the length of a dash-pivot is limited by your character's initial dash length. In order to pivot out of a full dash, you'd have to cancel it with crouch, dash again, and then pivot. So foxtrot-pivot
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