Nintendo isn't able to build a good phone. That would need tons of R&D, patents and whatnot. All things Nintendo doesn't have. Even their money is rather short for something like that. I mean, just look how a giant like Microsoft is struggling to compete with Apple and Samsung. They finally caught up with the Lumia 930, but they needed years and years of software engineering and they had to buy Nokia, which cost more than what Nintendo has in the bank to achieve just that. And while the products are of good quality now, the sales are ridiculously low compared to their competitors.

It's not like you can just say "money, lulz" and build your own smartphone. I mean, you could always build something by just sticking together parts, but that would be very dated and far far away from the build quality of iPhone, Samsung Galaxy and so on. They also wouldn't get away with slow hardware when building a phone like they like to do with consoles. The modern user expects one shitload of functions while everything needs to happen in an instant. No room for slow hardware or anything like that.

So no, it just won't happen. They would be better off selling licenses to Apple or Samsung so that those guys build some kind of Nintendo phone. But Nintendos own hardware studio just can't compete in any way with other manufacturers. They really should concentrate on software and should do only things that don't affect their other business. There are plenty of options, like some Mario games that are built around the gaming habits of phone users. A short puzzler or something, that would surely sell if Nintendos name is on it. There isn't just black and white, I think it's both a bad idea for Nintendo to just ignore the mobile market but it's also bad to go all in and leave their classic consoles behind. After all it all might just be a trend (the original iPhone is just seven years old) while consoles proved that they can make money for 30+ years. So it's much more logical to depend on the latter for Nintendos core business.

Oh, hell no! Handhelds with buttons are fine enough, thank you!

I don't think the hardcore fans, the ones that buy most of the games would like that. 

Not to mention that the smartphone market it's saturated. Nintendo would now have to compete with smartphones. It would even feel gimmicky, Nintendo would never take that risk because it's just not smart to do that when you keep selling so well with your own formula.

As for joysticks:
I have not tried it myself but I am very intrigued by the Steam controllers circular trackpads.
There can be other tech that can be used as joysticks, as improved 3DS circle pads, that make the design of the gadget easy to put in a pocket. At home it can be docked or connected to a more comfortable controller device.

You put out hurdles for this not to exist, therefore you do not see the product.   I do see someday the hurdles will be jumped.  My point is, Nintendo is not in the field where it can jump those hurdles you've mentioned, but for them to be relevant, they may need to.  There are companies out there who are better in position to do so.  With the ever growing importance the mobile field is garnering with gaming, it is not out of the question for the accepted gaming mobile to exist. 

And no, it doesn't have to appeal simply to those who use smartphones.  You're thinking to small and too early.  The progression of handheld gaming leans on the side of what takes less space in your pocket.  Or else you would have boomboxes still booming quaint neighborhoods.  The natural progression will be a combination of the two.  Who owns a walkmen and a flip phone and carries them everywhere?   No, that's backwards.  When the hurdles are jumped, we'll have an acceptable mobile gaming device that will be a phone.

I don't honestly think it will be Nintendo do get the combination right.  They don't have what it takes, but if they are still alive in the handheld market and they want to continue, they will eventually be forced to.  Look at gamecube, online wasn't a concern, but with the wii they were more acceptable with online games.  Wii half-assed online, they were forced to adapt with Wii U(Not by a giant leap, but for nintendo, pretty big leap) again. 

And yes, the cell phone market is saturated, but Nintendo machines will last 5 years, with small remodellings inbetween.  They don't have a small 1-3 year product release like other companies.  As long as they can sell upwards of 60+million(arbitrary, yet exceeding numbers) by the time their next machine comes in, it will be worth it.  And the games sold as well will contribute to the overall sales of the product.  Besides, machines don't sell machines, games do.

I know Nintendo can't.  But the combination of that machine will be out there some day.  It's just enevitable.  How Blockbuster was not able to stop online streaming, Nintendo may not be able to fight against this wonder gaming phone.  I think the only possible way this happens is if the first accepted machine comes to life, and nintendo would still be in the mobile gaming department.  That is the only way Nintendo can have this machine.

As for processing power:
the Nvidia Shield Tablet has the equivalent power and price of a Wii U in the body of an iPad mini.
This combined with circle pads and buttons and with basic wifi phone and browser functionality makes a cheap and versatile gaming gadget.

There are many smartphone producers that can help Nintendo with the phone technology. 

http://www.techinasia.com/2013-list-new-asian-homegrown-smartphone-brands/

They do not have to be bigger than Samsung or Apple. Nintendo will still be niche but with some of the functionality of the big brands.