I know little about ArcSystem but I praise the logic in this statement. I wish people would apply this logic to other third party companies as well.
Who was Kunio purchased from?
In 2015, Arc System Works obtained the intellectual properties of Technos Japan, which at the time were owned by Million Co. Ltd., which was created to purchase the properties of Technos Japan after they declared bankruptcy in 1996 (Here's the Wikipedia:
https://en.wikipedia.org/wiki/Arc_System_Works). They owned the rights to Super Dodgeball, Kunio, and Double Dragon. So it was more or less purchasing mostly dead IP without a backer. I personally would also expect Double Dragon to lead the charge on a beat-em-up representative just because of how much larger it was internationally and how it's generally considered to be the gold standard of beat-em-up games, but that's me.
Arc System Works started as far back as 1988, and they ended up making Guilty Gear in 1998, which would be the game that would go on to largely define them. Arc System Works has become synonymous with beautifully animated fighting games of high quality such as Blazblue, Dragonball FighterZ, Persona 4 Arena, and the upcoming Granblue Fantasy Versus. That's essentially what their brand has become most well known for in years and what represents them beyond all else, with Guilty Gear still being their baby and original title in many ways, though it's arguable about how far Blazblue has come since it was introduced. Either one of those two series would be your ideal way to represent Arc System Works for their own pedigree and IPs.
Kunio and Double Dragon are just specifically IPs you go for to represent beat-em-ups as very much the classic and most popular IPs in that genre of games. Thus, Kunio and Sol Badguy are characters that would be picked under entirely different circumstances and for different reasons despite being under the same developer. It's very similar to the question of the Microsoft rep; the reasons you would pick Master Chief, Steve, or Banjo & Kazooie were all vastly different and had little to no overlap beyond the company. If you're choosing to represent Microsoft, Chief is the clear best option as their mascot, Steve if you're going for the most broadly appealing game, and Banjo & Kazooie for the fans in Ultimate. Which one you choose is entirely reliant on your priorities prior to approaching the developer.
Unrelated to you, if we're getting a more obscure Japanese focused Sega character, I think Arle Nadja makes way, way, way more sense as Puyo Puyo is one of Sega's most popular IPs not in the game and Puyo Puyo seems to actually be doing decently well in the West these days, to the point where we've seen something like Puyo Puyo 2 available in the west for the first time through Nintendo Switch Online and several recent releases of Puyo Puyo as actual Puyo Puyo. The only issue I might see with her is moveset, but there are so many cool things you can do with a puzzle character that Sakurai hasn't had a chance to try yet, so I'm all in favor of her inclusion. I just would hope that Sakurai might tune down the hyper cutesy look I think she has in the more recent titles and reflect more of her muted earlier appearances, but that's me.