Well, Geno really is third-party so Nintendo would have to talk to Square-Enix during which SE probably would offer a better character.
Let me give you an overview of the characters that Square Enix has to offer:
1. Cloud-make a cameo as a summon in Kingdom Hearts: Chain of Memories on the GBA and that's the only time he's appeared on a Nintendo platform. Brawl also already four sword users and will probably have another 2-3 more. You also have to consider how SE could easily charge Nintendo an arm and leg to use him since he's so popular. In the end, why would Nintendo want to fork over a ton of cash for another sword user when there are probably several first/second party characters like Ganondorf, Marth, and Takamaru already waiting in line?
2. Sora- a copyright nightmare since he's owned by Disney (Buena Vista Games) and Square Enix. In order to use him in Brawl, Nintendo would have to pay both companies and go through a ton of red tape compared to other third party characters. It doesn't exactly help that Sora has only stared in one Nintendo platform game either so, needless to say, he definately wouldn't be worth the legal stress.
3. Black Mage and Moogle- Generic and not the stars of their respective games so therefore would not be all that good as representatives of Final Fantasy. Compare them to the likes of Megaman and Sonic and it becomes immediately apparent why they probably wouldn't be worth adding. ("But Fatmanonice, isn't Geno's situation the same? No and I'll explain why once I get to him.)
4. Chocobo- Basically a spinoff of Final Fantasy and what sense would it make to rep a spinoff and not the main series? There's also some problems with Chocobo's atamonical design when it comes to a game like Brawl but the first reason is the most important.
5. *Insert Playable Final Fantasy character here*-Some people have suggested people like Locke, Cecil, etc from Final Fantasy 1-6 since they were on Nintendo platforms but the problem here is how do you decide which one is the most important and therefore most suited to represented Final Fantasy in its entirety? Because, in general, the same characters don't appear in each new installment, this question because practically impossible to answer and left entirelly up to personal opinions. It's unquestionable that Sonic and Megaman should represent their respective franchises but it simply isn't the case with Final Fantasy.
6. *Insert Playable Final Fantasy Chronicles character here*- Same problem as Chocobo, why represent a spinoff and not the main series?
7. Crono- Sadly, yet another legal nightmare. Back in April of this year, Square Enix offically announced that Chrono Trigger would not be released on the Wii's VC or the PS3's Network anytime soon because most of the people who worked on it no longer work for them and the rights to the game are spread out all over the place (which is also why the 3D Chrono Trigger fan project was canned in 2004(? *I'm not sure when it was stopped but you can still see the trailer on You Tube)). With that said, Crono's chances of appearing in Brawl, let alone again, are insanely low.
8. Slime- A generic enemy for the most part and the star of a spinoff of Dragon Quest. Once again, why represent a spinoff and not the main series? Call me unimaginative but I also have an extremelly hard time imagining how Slime would work in Brawl considering how he doesn't have arms or legs.
9. *insert Secret/Children of Mana character here*-too obscure and ill suited to represent all of Square Enix despite being great character. There's practically no demand either and I don't think it'd be wise for Nintedo to "rent" and pay for a character that no one really wanted in the first place.
10. Geno- Geno is basically a Mario character so therefore is not suited to represent Square Enix as a whole so that automatically removes a ton of tension regarding that. In other words, adding Geno would be adding another Mario character and save them the trouble of deciding on someone to represent all of Square Enix. At the same time, he would still be a tip of the hat to one of the best third parties in the industry.
Nintendo and Square Enix have also made two joint project Mario games together in the past 2 years, Mario Hoops Three on Three and Ikari Street so it could be said the addition of Geno would tie into that. Back track about 9 years before that and we run into Super Mario RPG: Legend of the Seven Stars (the game Geno first appeared in) which was also not only Nintendo and Square Enix (then Square Soft) first joint project, but also Nintendo's first joint third party project on a major platform (Wario Blast, which was between Nintendo and Hudson Soft, was actually the first but that was on the Gameboy). That was pretty significant during that time because Nintendo was known as a company that didn't let anyone touch their games. Needless to say, Nintendo opened up in later years after that game with games like Mario Party (Hudson Soft), Donkey Kong Jungle Beat (Namco), the Legend of Zelda: the Minish Cap (Capcom), and F-Zero GX (Sega). As you can probably now tell, that was a very important moment in Nintendo's history.
As I have mentioned and several people have reposted from my Geno: Star of Heaven thread, Geno's legal situation is not the same as other third party characters because Nintendo basically controls the situation around him since SE can't use him outside of context (meaning a game not featuring Mario characters) or without Nintendo's involvement. Because of this, Geno is practically worthless to SE and has been sitting in a filing cabinet since 2003 after he appeared in Mario and Luigi: Superstar Saga. With that said, it should be a no brainer that Geno's "rental" fees would be minor at best compared to the likes of heavy hitters like Cloud and Sora. So in the end, Nintendo benefits because they get a unique and wanted character for peanuts and Square Enix gets recognized in what will probably be the biggest Nintendo game of the decade and get some money for a character that's been sitting in a shoebox under the bed and covered with dust.
Throw in how the third party barrier is basically broken for Nintendo/third party games (already explained in this post and previous ones too), how he's a very unique character and nothing like Smash has seen yet, has a decent amount of demand, has Sakurai's and developers interest, and could advertise SMRPG which is already the most wanted VC game in North America and Japan and you've got a character that knocks a homerun out of the park and really has no downsides.