I would love a beat em up rep and side scrolling shooter rep.
SpectreJordan
summed it up nicely but I will add that Streets of Rage 4 was recently on Switch so I see Axel Stone being a darkhorse pick. I also agree that Contra should be talked about more. It's a classic NES and SNES series that continued to get games over time.
People always talk about the same 5 or 10 characters but they don't bring up the Jimmys and Billys and the Battletoads and the Haggars. What about Arthur from Ghosts N Goblins? That was a well known game that was famous (or infamous?) for its hard difficulty. It was a notable game on the NES and continued to get games on Nintendo platforms. How about Frank West? People talk about Morrigan a decent amount but they don't talk about these other Capcom characters.
How about Maxwell from Scribblenauts? It's a decently popular series and Maxwell himself would fit so well in Smash and has effectively unlimited moveset potential. The series is owned by Warner Bros. so it's only big competition is Mortal Kombat which, while I would like to see get a character, would probably not work in Smash so he has no big obstacles aside from being owned by a western company.
Lara Croft too. She is brought up a decent amount but not nearly as much as you would think considering how iconic she is. For some reason, people seem to disregard her.
I could go on, but I would be here all day. The fact that people don't bring up these characters a lot baffles me. But I think I understand it. I saw a discussion on here about how people are drawn to likely characters and the more likelier a character is, the more likely people will want to support them. While I don't have any data to back this up, I think you can look at the trends and decide for yourself. For example, ever since the DMC games came to Switch ,Dante has garnered a much wider support base, But at the same time this line of thinking doesn't always work. Like I just said, people seem to disregard Lara Croft despite how popular and relevant she is. Would confirmation of her games coming to Switch be the final push to get people to take her more serous? probably so but at least to me she doesn't need any new games on Switch to be likely in the first place.
It's also bias too. Bill Rizer is not one of your wanted characters? Screw him, ______ is more likely than him.