I think PP tilts (especially up and down tilts) will ultimately be necessary for Pika to survive/win in neutral at the highest levels of play, once the meta gets more optimized. However, at the current level of play the vast majority of players can't do a damn thing against a Pika who abuses QA in any way that's not brain dead. The practice effort to reward ratio for PP tech isn't great at the moment. I would only recommend putting serious time into it if either you're bored enough with your solo pika practice that you need some variety in order to stay motivated or the rest of you're pika fundamentals (jab lock setups/execution, basic QA stuff, QAC/QALC, various gimping techniques, throw and up-tilts combos) are so polished that effort/reward ratio is now favorable. You're probably only in the latter scenario if you're a consistent deep threat at your weeklies, or if your name is ESAM.
One thing that's nice is that practicing PP's is easy to do while waiting for matches online in person. The mechanic requires no setup and is even brainless enough that you can practice one handed while having a conversation or half watching TV. Incorporating the tech into your game-play however, I find incredibly difficult. It's easy enough to pull off the 3 frame timing of PP's in training mode or against CPU's, but against skilled human opponents you need to be incredibly confident in your execution. For instance it is very easy for a retreating PP d-tilt to flub into a dash attack. So what was supposed to be a safe spacing tool and poke, turns into a huge and very punishable commitment that moves you in the direction opposite from what you intended. Compare this risk to the risk of flubbing a normal pivot grab, maybe you pivot tilt instead, hardly the end of the world.
But if you're planning on being a Hax-achu and risky frame perfect inputs don't scare you at all, then PP opens up a crazy amount of cool options for Pika. Dash dancing hasn't gotten much attention in sm4sh since a week or two after release people were calling it near useless as a spacing tool due to the fixed dash length. I think that people wrote off dash dancing much too early. Incorporating the ability to PP tilt out of a dash dance or fox trot gives pika incredible mix up potential and speed. One of my favorite options choosing PP dtilt in place of the retreating dash of a DD. Many shiek's and falcons have tried to dash grab or dash attack my retreating chu only to get hit with a dtilt jab lock or trip set up. The main reason you're going to learn to PP is probably going to be PP uptilt. Dealing with fast characters who can play a strong keep out and spacing game against pika (here's looking at you shiek) and with players who have downloaded your QA and T-jolt habits, PP up-tilt is one of your strongest tools in neutral. When an opponent respects pika's uptilt, it can be near impossible to land a raw up-tilt except as a punish tool. But the extra range that is gained from PP'ing (plus the fact that when you PP towards an opponent you'll hit with u-tilt's faster and more combo friendly rear hitbox) adds enough utility to the move that it becomes a valid aggressive option in neutral.
One other great use of PP comes in the form of PP shield. Now this doesn't require tilt controls to perform, so it's not super relevant to the thread at hand, but I think it's cool enough that it should be stated. One of the reasons pika is so easy to box out is because pika has horrible range OOS. If you notice a character like Ness trying to zone you out with well spaced SH fair's on shield, try a PP before you shield if you can read the jump. This spacing option should net you a lot more shield grabs and free hits with nair OOS. It's also great to punish landings.