I've got to say, I agree. I never really mentioned it, but I felt like it could be that way ever since we first saw Kirby be the hero, with Mario blasting away. There should have been an SSE Sonic meets Mario, and Kirby characters shouldn't have factored in as much in the game as they did, since they were the majority characters to actually advance the plot.
Basically, few things happen in the story: Characters meet, there are skirmishes, and the group(s) attempt to do something major against the SSE. Any time something happens that's not a meet-up or a small skirmish, it usually features a prominent Kirby character.
You mentioned Kirby at the beginning, saving a character, but you forgot: Kirby's strike is the one that shoots down the cannon. The one enemy ship is the Halberd, and capturing it could be considered a major subspace arc. If you were to divide the story into three acts, the first act features Kirby as one of the leading roles, the second Meta-Knight, and the third Dedede, maintaining focus on Kirby the entire way through.
And, of course, you mentioned the whole ordeal with Mario characters being treated poorly. Bowser is the SSE idiot, rarely succeeding against anyone, except DK in the beginning, where he was stealing bananas for no reason at all. Peach, while receiving great character portrayal, is like an entirely different person between the Mario universe and this one. Mario gets blown away at the beginning, and then is just another member of the huge, mostly generic anti-subspace army. Luigi receives that stupid scaredy-cat treatment, but at least it fits his SSB appearances before now. Donkey Kong, while rarely featured, receives a great portrayal, for what it's worth. Wario works alright, but like you said, Dedede tops him early on. Yoshi is just sleeping on a log and goes and fights.
Overall, the story was weak. I think that perhaps Sakurai inflated the appearance of his own characters, but I don't know if he intentionally left the Mario characters in poor light, or if that was just an effect of "too many chiefs, not enough indians." The SSE shouldn't have happened that way. What makes it worse, for me, is that there's so much filler in it. I can't see how it could have taken too long to create, aside from the bosses. It was essentially a game where you ran around and fought the same enemies with different backgrounds. I would have preferred to just watch cutscenes and play the boss fights over it, but overall, because Sakurai couldn't use everyone as true heroes, he just stuck his own characters in those positions.