Thing is, what differentiates the Paper Mario franchise from the Mario franchise? AFAIK It's literally the same world, but paper. At least with Yoshi or DK, the world's are heavily depart from basic Mario tropes. Even Warioware does. If Paper Mario were to ever make it, he'd represent the Mario series.
I got called by the poster to cover my taker on that argument so here we go
I don;t think the icon would change this much tbh. Cause really, both could happen and still be fine. If he has a different icon, that would mean that you would take the paper mario series as a separate branch of mario which tbh is kinda of accurate, but the other solution being a branch of the mainline mario AS the fact that paper mario is a parallel version of mario......is accurate too!
But if I break it down to character reps something bigger than themselves and this something is represented by an icon, both becomes possible. Except there's one thing that makes me think he would more have a mario icon: the actual fact of being a parallel version of mario. Of course, he's not mario, but being a parallel version makes him share similar category and similar origin even though they aren;t the same. it's just that idk why dr mario would be mario icon and not paper mario so if I take Sakurai as trying to be consistent in the icons choice, idk why it wouldn;t be the maro one at this point. I mean, even his stage is mario icon and tbh, it's not bad either, Paper Mario is a branch of the mario franchise, the different character would already do the difference, the icon isn;t necessary this much.
TL;DR: it's more likely because of consistency and the fact hat mario is a parallel version of mario that his series shares the mario icon.