Currently Online 
If it had the power and was easy to port to? Sure it would.
You bring up the Gamecube Madden games, but Madden kept making them year after year, till the Wii U came out. So they obviously were making enough money. Around 500K is probably fine for ports. The COD games on the Wii sold about a million each. Rock band and Guitar Hero both did really well on Nintendo consoles. There's also De Blob, Boogie, Epic Mickey, Goldeneye, and Rabbids, among others. Generally, solid games developed for the console did well. Of course there were some notable flops (poor red Steel) but a lot of companies found success.
While you're biasing this towards western games, there a lot of Japanese franchises that have done well on Nintendo consoles. There are six resident evil million sellers among the Wii and Gamecube. Soul Calibur and Tales of Symphonia hit a million each. Sonic has continually performed better on Nintendo consoles than others.
You're also ignoring the fact that a big part of the market has neither embraced the XBox One or PS4. Children and casual gamers just haven't gravitated towards the PS4. Aside from Minecradt and (debateably) Little Big Planet and Knack, games for this audience just haven't done very well. I know people will pull out the old "casuals stopped caring about the Wii" thing, but even last year, Just Dance hit over a million, selling better than all other versions combined. Skylanders performed best on the Wii through 2013. The Lego Franchise took a huge hit with the failure of the Wii U. Market fatigue of course played a large factor in these drops (far more than iphone games and such I'd argue) but I think some companies are really missing that market Nintendo once provided. It's not a guarantee that they can recapture it, but if Nintendo makes a big splash initially, I think these companies would try to capitalize.
If it's relatively cheap to make ports, and the NX gets a good start out of the gate, there wouldn't be much reason to not make games. The Gamecube got decent third party support despite middling sales because it was fairly easy to port to. The Wii started losing support because they had to make games from the ground up instead of porting. The Wii U didn't get support because people figured out pretty quickly it was a dud and the install base was awful. If Nintendo has comparable power and a decent install base, it's hard to see why it wouldn't get decent support.
