I'd argue a few characters get one or two - while not aesthetically - largely different customs that make enough difference to change up their gameplan. But Palutena is still definitely the biggest example of differing customs because they're so drastically different from eachother both in how they're used and aesthetics. The key notable one being Lightweight > Counter which can hop her up multiple tiers.
In a way, I feel Pit did get quite a bit of attention. I'd argue Pit is one of the more balanced and well-rounded characters on the roster, and the fact that Sakurai even bothered to put Dark Pit in is a testament to his bias. However, it kind of backfired since Pit's strong neutral play-style doesn't really put him in an overtly powerful spot like it was -- in my opinion -- likely intended to.
If you were talking about it in terms of customs though, well, simply put, Palutena is the one with the largest toolkit in terms of canonical abilities. From Warp all the way to Celestial Firework, all her customs are abilities that she controls. To leave one out would feel weird, and no other new character really has that kind of trait except maybe Mega Man, and arguably he did get some pretty drastically different customs (At least, IMO. Though I know some Mega Man fans were disappointed with his base moveset. Never mind his customs.), it's just likely that they thought of implementing Palutena's customs first.
That said, if you want a really cynical answer - Palutena is Sakurai's waifu. ¯\_(ツ)_/¯