Third-party companies that get a representative in SSB4 should be both of these things:
1. Iconic and a true giant in the industry
2. Has had a strong presence on Nintendo consoles delivering great games to them and/or have a good relationship with Nintendo
I think the three third-parties we've had thus far fill both of those criteria. Sega have been consistently bringing titles to Nintendo consoles, a lot of which are exclusive to them, since they stopped making consoles themselves and have had a strong relationship with Nintendo creating collaborations such as the Mario and Sonic games and F-Zero GX. Konami have brought a lot of top class and iconic games to Nintendo consoles throughout their history such as the Castlevania and Contra series. The same can be said for Capcom even moreso with the classics that the company has brought to Nintendo consoles rolling off the tongue - Mega Man, Contra, Resident Evil, Okami, Viewtiful Joe, Street Fighter II, Monster Hunter, Final Fight, Bionic Commando, several Zelda titles...
What other companies fill that criteria? The definite one is Square Enix. Their CV on Nintendo consoles is stunning. Final Fantasy (including the main series, Tactics, Crystal Chronicles and Chocobo), Chrono Trigger, Secret of Mana, Kingdom Hearts, Dragon Quest... then there's great collaborations they've done with Nintendo, most notably Super Mario RPG, but also the Fortune Street games, Mario Hoops and Mario Sports Mix. Their a massive company, the games are there, the history is there and the relationship is there - Square Enix would be the perfect company to give a character.
Namco would be another obvious choice. They're not so strong in the games department on Nintendo consoles with their classic games such as Pac-Man and Dig Dug being more famous on the arcade and their more recent games such as Tekken being more prominent or exclusive to other consoles. That said said library is far from bad with their arcade games also available on the NES/VC and series such as Mr. Driller and Pac-Man being prominent on Nintendo consoles. Their main selling point for me is their relationship with Nintendo - the company have had a number of high profile collaborations over the years including Pac-Man Vs., Star Fox Assault, Mario Kart GP series and of course SSB4 itself.
Everyone else is kinda sketchy. Hudson comes to mind, although do they count as their own company now that Konami own them? Aside from Bomberman, have they delivered enough classics to Nintendo consoles? Ubisoft perhaps, although I don't think they have a strong enough history or identity especially on Nintendo to warrant a character.
Those are the only companies I'd consider personally, all the rest I'd rule out for not fulfilling that criteria. What does Sakurai think and who would he prioritise? Who knows? Heck, he probably doesn't even know himself.