Yes they will beat every single garbage game on smartphones and start a new golden era of casual gamers, and maybe more and more quality games coming to smartphones because Nintendo come to compete.

"BUT THEY NEED TO DESIGN GAMES THAT WORKED FOR TOUCH SCREENS "

Your assumption is based on fallacy that making better gameplay = getting better sales, I was told by guy from industry that having complex gameplay is actually detrimental to mobile games, ideally you should have nice presentation and effective monetisation with just enough gameplay to rout people from first to the second.

I wouldn't be surprised to see smaller teams within Hal Labs or Intelligent Systems give it a go. But as for Zelda, do you really expect EAD 3 to work on this platform? I think they would let a third-party handle it, in which case I would expect something more along the lines of Four Swords than a full-fledged handheld Zelda.

Brain Training is a no-brainer. Hah. Several of these are, but I singled that one out for the sake of the pun.

Actually it's based on several factors outlined in the OP. Gameplay is one, but Nintendo could make an absolute turd Mario iOS game and it would outsell 95% of the smartphone games out there just because it's Mario. 

A Nintendo phone would definitely be a fresh thing. Just imagine a phone without micro transactions!

I fully expect Mario Kart to be on smartphones in some form eventually.

How mighty has fallen. Sorry. I want Nintendo to do bad in mobile and well in consoles.

It already is

i think all depend on prices.
if they will make the deal: free with ads, pay for no ads, demos, etc.

but i trully can see the potential there.

A Splatoon iOS game too ... obviously wouldn't be like the Wii U game ... but I can soooo see that.