Double pivoting is good for when you want to move a small space forward and do a standing attack quickly where wavedashing is too slow because of the airdodge recovery frames, and when you have to be facing the opponent. And when that attack is not a grab, up-B, forward B, or up smash or else you can do it out of a dash anyway. And when you absolutely have to be facing the opponent; a single pivot into reverse f-tilt or f-smash works fine for those attacks. So that leaves...
-jab
-dtilt
-dsmash
-utilt
-no-momentum short hops, which allow for controlled spacing or fade-away fairs, nairs, or maybe uairs. Might make "crossups" more ambiguous too.
Pivoting into up or down tilts quick enough to be worth the speed of the the double pivot is prohibitively difficult. It would be amazing to have utilt always in your back pocket, though.
Double pivot could also allow you move forward without ever needing to leave your initial dash, allowing you to safely dash back any time you want while moving forward.