Okay, I can concede up front that Captain N is unlikely to get in. I can even concede, upon rewatching the show all these years later, that the show sucked.
Despite that? Captain N could make a very interesting Brawl character and we could even make a whole new gameplay mechanic for him: Power-meters/recharge-times. In the cartoon, he could use various NES controllers to do amazing things; super high jumps, long horizontal dodges, shooting lasers at enemies (with his NES Zapper), and so forth. But he was limited by one thing: The more of these actions he did, the lower their power got. Eventually some of his equipment would run out of energy, leaving him with purely his human physical talents to get by until they recharged.
You could do the same in Brawl. Let his B moves drain a power meter (set above or below his Damage Percentage indicator, of course) that slowly recharges over time. These moves are really good moves; very impressive Up-B Third Jump, an excellent projectile in his Zapper, etc. etc. But they recharge fairly slowly, and his normal (A, Throw, etc) attacks aren't all that impressive. So he'd have a game plan centering around careful use of his impressive special attacks, and defensive play while he recharges them.
"He wouldn't be Tier 1 if he's designed like that," one might retort. That's okay. He could serve as a learning curve due to this, helping encourage people to understand various aspects of Brawl.
Is he likely to get into Brawl? Of course not. But there could be plenty of legitimate, interesting, gameplay-worthwhile ways to put him in the roster. Sometimes mental exercises and thoughtful "What If?" lines of logic are fun.