There are franchises that sold well but never got another sequel for unknown reasons. A good example of this is Kingdom Hearts 3.

But that franchise is HUGE. There is no way nintendo could buy an exclusive sequel for that. I don't expect Nintendo to drop a bomb and buy a huge franchise, but if they continue with what they did with bayo 2, they could really bolster their library. Titles like that don't sell fantastic, but if you want to get gamers on board, and establish good will, then this is a great strategy.

how about sega in general 

Definately, Sega is not only bleeding money, but a shell of it's former self talent wise. Nintendo has a lot of money and a lot of talent. Sega has some great, crazy cool IP's that are not being made. Make the connection.

I too want to see a fps, timesplitters be perfect.

TImesplitters would be tougher. I would love it, but with Bayonetta, and the games I've mentioned, those are all eastern games. Nintendo really only works with eastern devs. I just don't see them putting the time to help fund and develop a western game. Let's face it, Nintendo has it's priorities set firmly in the east.

Great suggestions, guys. I would love to see some of these games on ANY platform.

@OP: What about Prince of Persia? Not sure how the GamePad would help much, but that could make a splash.

That franchise is huge, yet it looks like S-E thinks that their time and resources are better spent in other games. Nintendo could put the extra money (and devs) S-E thinks its needed for another Kingdom Hearts game to be worth it.

Actually getting Kingdom Hearts would be cheaper on the long run than Shenmue, as Shenmue games are ridiculously expensive to make, and it will sell more.

You need big sales from a third party to convice other third parties that there's money to be made in your system, and nothing better to do that than a big franchise. Monster Hunter and Zombi U can't do everything by themselves.

Nintendo does have the money, they got Resident Evil two gens ago.

EDIT - That being said, I think it's better for Nintendo to get talented devs and let them make new entries of existing Nintendo franchises that aren't being used at the moment.

Resident Evil was a special case though. Nintendo didn't really pay for that, to my understanding. The dev's were frusterated with the PS2, it being the weakest console. The gamecube was significantly more powerful, and the Xbox was essentially dead to Japan. With Nintendo being so strong in Japan right now, I could see KH3 coming to Wii U, but it's just a bit more of a stretch than some of the others. 

Shenmue 3 would be a big hit.
Still I think they could do is to get an exclusive deal for Blizzard games like Diablo or World Of Warcraft, those game, while unplayable with a standard controller could fit well on the new controller.