"Heavy-affiliated-with-Nintendo third-parties" is an irrelevant criteria that needs to die out already. It doesn't matter most of the time. We literally have only two with content that remotely relates to having a Nintendo presence; Super Mario RPG and Bayonetta. The rest got in on their own merits as being gaming icons.
Sakurai doesn't care and never actually did. Nintendo might, but that doesn't mean it's that important. If a 3rd party is chosen, it's still going to be because they're important too for who they are. Cloud got in because he's the mascot of Final Fantasy and a gaming icon. It was pretty irrelevant that FF started on Nintendo. And Cloud had barely cameos on the Nintendo games. To pretend he's heavily affiliated with Nintendo is ludicrous. He isn't nor ever was. He's finally got his actual game on Nintendo, but that was well after Smash Ultimate's roster was decided too. He didn't gain any legitimate relevance to Nintendo till well after Smash itself existed, and especially after Smash Ultimate was completely finished being figured out who the base roster was. The closest thing Sakurai has said on the issue is that he wasn't sure what he would've done if Cloud had no Nintendo appearances. And that's cause... gasp... it wasn't an issue that came up at the time. So he had no actual opinion on it. In other words, it was a relevant criteria to begin with.
Just like it never was. Bayonetta is a special case only because we don't know how she got chosen to be in the game in the alone. We know she's been worked on and licensed way before the ballot(no way they can get that done in two weeks, let alone that would mean if somehow that's possible, they had to have a ton of votes from her day 1, and somehow magically get all the licensing, full body work and modeling done... in about 13 days). It's not feasible. Being an exception to the rule of 3rd party icons is fine. But why she was an exception is unknown. Geno is well known why Sakurai chose him; fan requests. That's pretty much it. Geno however isn't playable(yet), so that didn't do much beyond get him to exist in the game in smaller roles than playable or assist anyway. That's important to remember here. Of course, yes, Nintendo might only choose those they can promote. Whether it could be from an upcoming FF game release, Slime for DQ(I don't think Erdrick even has an upcoming game? Though Jade might?), or just for re-releases. DLC being promotional makes sense. Though it doesn't mean an affiliation with Nintendo so much as a game upcoming that will be on Nintendo later. Affiliation with Nintendo means they're effectively known as a Nintendo character by fans(Geno, Simon, more or less just about everybody but Cloud, really. But those were coincidences for every 3rd party but possible Bayonetta, so it's a meaningless thing to look into). Of course, appealing to Nintendo fans is a very very different thing from choosing a character simply because they had a ton of Nintendo games. That's not how you choose gaming icons. Like, at all.