IMO, gimping/pushing an opponent out of bounds is the reason to use Piercing period. It's not going to ever get outright KOs like standard sphere would, it just doesn't do that much pure knockback. It can, however, carry people away very easily.
On stages like Castle Siege, you have that walk-off transformation. Piercing Aura Sphere has the potential for low % kills from full screen, even despite the existence of the statues in the center. It's incredibly fast speed makes it difficult to reflect too. Pit's guardian orbitars do not come out fast enough to reflect a fully charged PAS on reaction, he has to activate them pre-emptively.
One of the main problems Piercing Aura Sphere faces are that while it eats any other projectile, it gets stopped easily by almost any A-move it clashes with. If you can punch the piercing sphere in time, it'll clank, then pass through you without hurting you. That said, it's like trying to punch a bullet since it's so fast. So, moves with long active hitboxes can keep people safe.
Another problem is that the aura spheres are smaller. Because of this, they don't snag people as well, and require more precise aim. Standard/Snaring get large enough that they're the size of some characters in the game. Piercing Spheres can be hard to hit against smaller characters like Pikachu or Kirby.
While Piercing spheres do less damage, they're a lot more spammable, and you can chuck these from across the stage repetitively. At max charge at 0%, it's only 4% damage, but it's so easy to land, it's not the biggest issue. Piercing Spheres intercept people all the time if they charge at you.
Also against slower characters, I prefer Piercing over Snaring simply because slower characters usually have awful recoveries, bar like, Charizard. If a character like Ganondorf or Bowser gets hit by Snaring, unless it kills them outright (which is difficult due to the vertical knockback against heavy characters), they don't really lose the ledge. If hit by Piercing however, it can carry them just far enough that it's literally impossible for them to recover. It's also easy to hit with since those characters have big hurtboxes. Thanks to the speed of Piercing, it's also tougher to air dodge through.
Despite my enjoyment of Piercing Aura Sphere, the standard sphere is definitely more versatile. The Aura Sphere charge shenanigans you can do for movement can't be done as easily with PAS due to the smaller sphere size. The damage build up is slower, meaning standard sphere has greater returns most of the time. Off-stage gimping/KOs can also be done with regular spheres. Though it's slower, it's also bigger, clipping a lot of characters in the head and, thanks to higher KO power, outright ends people.