As a correction, they aren't character action games. DMC4 and Bayonetta 2 are character action games. Those typically focus on a handful of characters and technical combat that is focused on what your character can do with their moves as defense, whereas beat'em ups/hack and slash games have a lower skill ceiling. I don't think I've ever heard anyone call SB a character action game, expect when comparisons to DMC are leveled, which still doesn't matter because the focal points of the game are more in line with beat'em up design mentalities.
Segmented levels, a singular focus on wailing on a lot of guys rather than a strong few with little diversion, etc are all different than the longer, more exploitative experiences found in character action games.
The Tekken Advance comment doesn't really make sense. You could portray SB as a sidescroller and the only thing it'd lose would be certain attacks. Seems like you are focusing more on the fact that Advance was made and SB-sidescroller wasn't rather than what makes SB not a beat'em up.
Powerstone itself carries a bunch of things from SF. It's different because you use items, move on a 3D plane, supers are activated via items, and it's 2-4 players at once. But the same design principles can be applied - players who employ a good neutral game, use normals effectively, and time their combos right will come out on top. It's made that way because it's a fighter, and that umbrellas a lot of things. No less invalid, just as SB is umbrella-ed under the action genre with FF.
I also think you are too focused on perception and the unwillingness for people to try something different, or "evolved". I've dropped a ton of hours into countless beat'em up games over the years. I've watched the sidescrollers get less and less, and with that, the design elements that made them so great not transition to 3D. That's fine - not all of them can do that. But SB hasn't lost much of anything during the move.
At the end of this whole conversation, and this goes for genre shifts in general, people forget how things have changed. Sidescrollers were far more basic before Final Fight, and you could make an argument about how the push for super moves, weapon usage, and button inputs (like in Battle Circuit) are pretty large changes for sidescrollers as well. That might be smaller than a move to 3D, but having to do a hadoken motion when not playing a fighter is just as eyebrow raising as purposeful dash canceling.
tl;dr The same design mentalities are still around in DW, SW, and SB style games, they've just morphed into something different while keeping the core of what beat'em up games used to be like. If someone asks for another sidescroller and just that, don't show them these games, but if people are willing to try other things ala Tekken and SF (or Powerstone, which is still a fighting game despite how it plays out), then it's not going to harm them.
