TBH I've never understood the huge pull Geno has in core Smash fandom.
Like, people can like what they like and I'm not saying that's a bad thing, but for me personally...I've never understood it. I've personally never found Geno to stand out in the way people say he does.
To each their own though, of course. I'd be happy for others if he got in.
I can't remember who pointed it out, but there's one really good analysis that could point to "why."
The Mario series is one that appeals to people of all ages, including children, given the abundance of colorful characters. However, in general, RPGs don't tend to be appealing to younger children in the same way (not to say there aren't exceptions...just look at Pokémon) since they're more story and dialogue driven. Super Mario RPG is a game that bridged that gap for many people growing up.
As for Geno himself, he's this mysterious and mystical badass who deals a ton of damage (but also has his more dorky, lighthearted side). That general archetype appeals to a lot of people, and almost all successful RPGs have someone like that.
But for a lot of people, especially those who got into JRPGs with Mario RPG as their first, Geno was the one to introduce that archetype. So he made a lasting impression on those people likely because to them, he was the first one.
tl;dr, for a lot of people, Mario RPG was their first gateway RPG, and Geno is a character from a popular RPG archetype, so he made an impact on people in their formative years.
At least, that's one explanation.