The main producer of the Team Ico projects has stated in the past that the main inspiration for his titles is Zelda. Secondly, all of Nintendo's competitors try to copy their IPs in the same manner as their gimmicks. All of Sony's platforming games are trying to appeal to Mario fans. As for not wanting to compete with Nintendo's IPs, they all ready do it, but on a more subtle manner.
Have you actually played Team Ico titles? They're nothing like Zelda. They have a high emphasis on puzzles, more than any Zelda game. I can't really compare Team Ico games to anything else on the market. They make niche games. They're not going after Zelda fans.
The rest are very different platformers than Mario. I wouldn't say they're so much as trying to appeal to Mario fans as they are trying to make a very different kind of game than Mario. Sony can't just make Mario games with a different character running around. I suppose, in a way, one could say that Sony's answer to Mario is to make something that is decidedly
not Mario by adding stealth or third person shooting. If that's the case, they aren't trying to swoop in and capture the hearts of Mario fans because that's just never going to happen. They're trying to carve out they're own audience that can co-exist with Mario and they're doing it by not making the same kind of games.
Nintendo has stated they wish to appeal to core gamers with the Wii U ans what better way then capture better third party support? We all know that the only sure fire way to capture their support is for Nintendo to show them how serious they are out having their partnership. The best way to do this is for Nintendo to have a core title of thier own. The market has shifted to the point that the best core titles are made by western deveopers. The last time I checked Retro was a western developer, so why not let them make a core FPS title for the Wii U?
Wait, so you mean to tell me that your idea for Nintendo to cultivate partnerships and show 3rd parties how serious they are about having that support is by using one of their best development teams to create a FPS that directly competes with some of those companies biggest IPs? 3rd parties having been bitching for years that Nintendo fans only buy Nintendo games and you want Nintendo to make it even harder for 3rd parties to succeed on Wii U. Right.