Even then, my point still stands. The reaction videos even say it for themselves. "How is this possible?" "No one thought it was possible!" "He hasn't even appeared on a Nintendo console!" Pretty much across the board people never thought it was possible because of the history behind FFVII.
And while you yourself may not think "history with Nintendo" doesn't matter, it still has a fair amount of factor, to a degree. Snake and the Metal Gear Solid IP might've pushed the boundaries, but you can't deny that he has at the very least SOME connections with Nintendo. Every third party guest has connections with varying degrees, which makes them not feel as outlandish as say Katalina or Master Chief.
Snake was in because it was asked. It had jack-all to do with Nintendo. Sonic didn't get into Melee due to the fact it was too late into development. Nothing hints at Sakurai giving a rat's ass that Sonic had zero Nintendo appearances at that point. People need to let it go. Them being an iconic character was the reason they're getting in, not some Nintendo appearances. Bayonetta's your exception. If Master Chief isn't getting in, it has jack-all to do with some "hasn't had his game on Nintendo/barely was a costume". It's because Microsoft doesn't want their character on an opposing console. Which is fair, since Halo is 1st party and not meant to be on something beyond PC/Xbox.
The fact that so many people genuinely thought Decidueye would get in over Incineroar should tell us that choosing the most important/most promoted starter isn't always black and white.
Like you said, the Champions are all equally important, no disagreement there. That being said, it's extremely generous to say we could unanimously pick out who the most important starter in each Gen is. Would most people agree that Infernape is the most important Gen IV starter? Is Emboar hands-down the most promoted Gen V starter? Yes, you do have some exceptions like Charizard, but that's really the only good example we have. Greninja and Incineroar were chosen long before Sakurai had seen any implication that they'd be pushed over the other two starter Pokemon (and with the latter, there's barely been anything from TPC aside from a few minor roles in the anime that's indicated that he's more important).
Perhaps there's a slight difference between Champions and starter Pokemon, but I don't think it's fair to call it a poor comparison, especially when both Champions and starters all share an identical role in their games. You could add any Champion or starter in Smash, and I guarantee you people would rationalize why that character makes so much more sense than the others.
No. They constantly promote different Pokemon starters over one another. It's a poor comparison and always will be because promotions don't work that way.
The "important starter" is chosen for your playthrough from the beginning. Gamefreak chooses the most important starter to promote. Decidueye barely was promoted. Primarina was barely promoted. Incineroar had tons of promotion. So did Greninja. That wasn't so much the fact they became the main starter for people to know, but Sakurai chose the characters who also were intended to be important in the anime. They were factors. He already is well aware those Pokemon aren't all treated as equally promoted. He actually pays attention to what Pokemon is promoted. There are exceptions, obviously.
The reason Pokemon isn't comparable, is that Sakurai also doesn't choose Zelda characters from concept art only. He actually set aside a slot for Pokemon and Pokemon only. He isn't going to do that for the Zelda series. That means he has no reason to choose a Champion that way either. None can stick out at this point, because all he sees is 4 equally promoted characters. Coincidentally they're all Stickers.
And you're wrong about Incineroar too. He had concept art that literally showed him hanging out with Ash. He already knew the character was going to be promoted. Only Incineroar was shown hanging out with other trainers. The other two were just shown by themselves(and pre-evolutions). It doesn't mean he would've guaranteed chosen Incineroar, but yes, he was well known as being a key promotional factor. Something the other two were not.
It doesn't mean it happens all the time with every Pokemon, but they've been doing it for a while now. And they're going to keep choosing a Pokemon to promote for the anime because it's an advertisement that works. People know the anime. Ash is way more known than Red too. It makes sense.
Greninja actually did not have art that promoted him as clearly being part of the anime. We don't even know if Sakurai knew that already. But he's an exception here. However, being as Sakurai doesn't look at concept art that early on when choosing characters except for Pokemon, it means, again, this is irrelevant to the Champions. Unless new promotional material pushes one as more important, they're just a group that belongs together and is hard promoted that way. It makes way more sense to just treat it that way and not try to make one more special when choosing Smash content. Having them all as Spirits is very logical.