I don't think Spring Man will have as much support for the next game, given that he's officially confirmed to not technically be the protagonist. Many will still want him for being the mascot, or because they like the character, but now there's not much really saying that he 'should' be in. If the comic comes out, though, that could affect things, given that he's the protagonist in that. Spring Man also gives the option for an easy Springtron echo, so if they wanted to add multiple ARMS characters, this would be an easy route to take.
Now that we have a 'normal' ARMS rep, the door seems more open for the unusual reps like Helix or Twintelle. Twintelle especially has a ton of popularity, so she seems like a fairly likely choice for the next game. Ninjara and Lola Pop also have a good amount of popularity, so I wouldn't be too surprised to see either of them (especially Ninjara, now that we know that Sakurai considered him already).
Assuming that Coyle's role gets expanded in a sequel or the comic, I could see her popularity increasing. People tend to want villains in Smash, and though Coyle is the villain of ARMS, she's pretty underutilized. Though she's heavily tied to the lore and story, she only actually makes one appearance, and it's on the highest difficulties, so many might not even encounter her story role. For the most part, she simply serves as a backstory for other characters and aspects of ARMS. Her design and personality seem to be pretty well liked, so if they made her a full on important villain, I could definitely see her support growing.
I feel like the opposite might be true for Max Brass. Many have speculated that he'll be replaced as champion by Min Min in the sequel, and if that's true, he'll lose the big thing that makes him stand out from the cast. Sure, he's still got a cool design and he's a well liked character, so he'd still have plenty of supporters, but he'd no longer be that significant to the ARMS world. He'd just be another fighter on the roster. Of course, this is all in the hypothetical circumstance that he gets replaced as champion. If he stays champion, his support will probably continue to grow.