I'd say Reyn's Driver is the inverse of it; Rather than a sword modified to also act as a shield, it's a shield with a pointy bit on the end.
I'm having trouble following the train of thought here so I might have misinterpreted something.
Paper Mario may have a completely different gameplay style by nature (unless you're Super Paper Mario), but it still involves the same characters (the protagonist doesn't even shift to someone else) and enemies, with additions either being stuff you could see being in the mainline stuff or just slapped on there because reasons (unless you're Paper Mario: The Thousand Year Door, or Super Paper Mario). Beyond that, it's simply not big enough for it to be considered it's own franchise separate from the Super Mario franchise.
As for it being considered a separate series in Super Smash Bros., well it already isn't, but barring the cop-out answer, it wouldn't really make sense to have a new series where the only character is another version of Mario. Why would said character not be a Mario character?
It has a ton of unique enemies that never appear in Super Mario, so... not all the same. It veers off from the norm massively, at least compared to Mario & Luigi who only has a few unique bosses at best(and a tiny slew of unique monsters), but otherwise, mostly recolors of previous characters(not unlike Super Mario RPG). Now, Paper Mario still uses a fair amount of regular species, but even in the first game, has its own unique creatures.
Paper Mario is an entirely different universe anyway. That alone is more than enough reason for it to get its own symbol. It's not Super Mario in itself, it's Paper Mario, starring a different universe's Mario entirely who even teams up with multiple characters who has zero relation to Super Mario even as a species alone. A big thing to remember is that while it shares some species, Paper Mario went out of its way to make a ton of new ones. It's not till Sticker Star where they're forced to use mainly regular Super Mario characters as an annoying mandate, and that's also when Paper Mario teamed up with Mario and Luigi themselves. As well as Paper Bowser met up with regular Bowser. The Mario & Luigi series are the same as the regular Super Mario universe. They intentionally separated it in PM only. That alone, is, yes, enough to get one's own symbol. Since it's a symbol that also represents their own universe(just like WarioWare or Donkey Kong Country, both fully connected to Super Mario... moreso than Paper Mario is as a universe, anyway).
The Paper Mario spirits are listed as part of the Mario series. Enough said.
That's not a good argument and is completely dismantled when that's how Wario started out. A Super Mario trophy. ...And when he joins, his own standalone universe. There's precedent it can happen, from the same base series no less. How they're listed as stuff like trophies and spirits don't relate very well to stages(we barely have one of these) or what games they directly represent, or how unique the games are.
Paper Mario is very unique and can easily be its own universe. Likewise, it can work fine under Super Mario too. Both are legitimate ways to go about it. It overall depends upon the content in itself. And how Paper Mario is represented. You won't see Mario fold himself(he actually can't do that, though he can come close with some power-ups in Galaxy).