Missed a lot of discussion. Fundamentally I agree that Spring Man is the most likely, but we shouldn't dismiss other possibilities yet.
"Mascots and Protagonists get into Smash"
I doubt there's any such rule when deciding a Smash character. The characters that are getting in do so because they're notable and someone at some point agreed they would be fun and could be in the game.
We know how decisions happened with other characters, but we don't have enough information on how the arms decision took place. It's possible someone at Nintendo requested an Arms character, and it's also possible that they specifically pointed at Spring Man or someone else. But we don't really know, and in that context the circumstances around the reveal and the development time of the character begin to matter more. Circumstances like "what would the Arms producers ask from Sakurai?", which leads me to the next thing
"Popularity is not as important as being the protagonist"
My main counter to this is that while Min Min has popularity going for her, the results of the party crash bash are not exclusively that they prove she's the most popular.
To me the most significant thing about the crash bash is 1) we have reason to believe devs could follow the splatoon model of shaping future content based on the results of their final event, and 2) this event took place in very very close proximity to the timeline around where the character would have been chosen (mid-2019).
If would be not unlikely that in an attempt to decide which character would represent Arms best the Arms producers would lean heavily on the results of this final pcb, nor would it be unlikely that in seeing these results publishers figure that this would be the character most likely to bring attention to Arms and Arms x Smash
and a more specific argument I saw:
"Edelgard was more popular but byleth was chosen, showing popularity doesn't matter"
This is an interesting one, but I think we're talking about completely different beasts. If you play Three Houses you have a 100% of learning about Byleth and going through their story. I figure when trying to decide a character before this game was out they didn't have reason to believe Edelgard would be more popular than Dimitri/Claude, so the safest choice was Byleth with all their weapons. Remember Sakurai played this one before the game came out, he couldn't base a decision on popularity realistically.
More on this, I think polls have gone to show dimitri being the most popular, with claude close behind. Edelgard to me still would make sense because of story reasons I won't spoil, so while in a way I agree, I also think it wasn't trivial that she would be the most likable choice of the three lords.
Again, I don't disagree that Spring Man is the most likely, just because it's the simplest solution to adding Arms in smash. But this wave of "yea, Min Min being popular doesn't matter" fails to understand why she seems so possible in the first place. It also pigeon-holes Arms as something established and defined where it's far from being the case. If anything it looks like they're very intent to keep open the possibility for more lore than originally... remember that dark horse comic? The preview began with huge focus on Spring gym and the Spring Man line. But then that comic still hasn't come out. How do we know they're not revising what they want the lore to be based on what the response wound up being? How the story develops and what characters get pushed and not is still up for grabs, the franchise is young.