Third party. Nintendo's most legitimate consoles had good third party support

Probably not.

Limited functionality? Smartphones have absorbed the functions of dozens (hundreds?) of single-purpose devices/services:

• Communication methods: home telephone and land line, mobile feature phone, postal mail, walkie-talkie, whistle
• Life stream recorders: diary, camera, video camera, audio recorder, ancestry history recorder
• Social lifelines: social communication by blogs, Twitter and other microblogs; Facebook timeline; photo-sharing services like Instagram; email; instant messaging; social GPS tracking (to find your friends nearby)
• Personal organization: watch, alarm clock, personal planner, social calendar
• Personal productivity: calculator, GPS navigation system, compass, calendar, address book, dictionary, thesaurus, white or yellow pages directories, car keys, bank ATM and teller (to do banking, send money, pay for things and even deposit checks)
• Entertainment: music player, game console, radio, TV, remote control, TV set‑top box, VCR and DVD players
• Knowledge hub: news feeds, sports commentaries, community forums, weather forecasts, general interest topics (for example, astronomy, cooking and so on)
• Personal travel and entertainment guide: instant foreign language translator; currency converter; restaurant, hotel, attraction, movie and transit guides; augmented reality city guide
• Personal health guide: real‑time auto accident monitoring, and with specialized attachments, the ability to monitor heart rate, blood pressure, blood glucose level
• Personal shopper: price comparison tool, product specifications, community reviews, coupons, classified ad listings
• Existing technological devices: notebook, desktop, netbook, tablet (including home Internet service), scanner, answering machine, printer, wireless router
• Reading materials: books, comic books, recipe books, magazines, newspapers, entire libraries
• Teacher: courses with every personal or business topic possible, just-in-time video education
• Business devices: cash register, employee time clock, filing cabinet, building or room access card
• Business productivity: memo audio recorder, notepad, meeting planner, meeting reminders, to‑do list, address book, PowerPoint presentation controller, business cards, networking and social events, project management, social customer relationship management
• Items in your purse or pocket: make‑up mirror, pedometer, wallet including credit cards, debit cards, loyalty cards, gift cards
• Tools in your toolbox: flashlight, measuring tape, level

True but they need 3rd parties that make sense for them and ones that will differentiate them from the others. Simply getting ports won't do the trick, not saying they won't help but people very seldom buy a Nintendo device for playing multiplats. 

In theory there is no reason against it. They clearly have (and had) the chances to make another succesful console. However, in reality, they'll fall over themselves as always and fuck up a lot of things.

Nintendo really probably has their hands full just maintaining their handheld market, it will take a minor miracle for that not to continue to drop. That's where their focus has to be.

Consoles are ... tough. Nintendo could create another really successful home console ... but technically so could Sega.

Realistically ... not without a miracle controller, and even then, in today's market, that likely would be copied very quickly (MS and Sony inexplicably gave Nintendo 4 years all to themselves basically with motion gaming whereas the N64 controller was copied much more quickly).

Sony is too strong in the console market and they appeal to *everyone*, you have to to be able to sell the amount of systems they sell every generation. Even in a "down" generation, the PS3, they'll end up selling 90+ million consoles, which just about equals Nintendo's best generation and in the three other console gens they've demolished Nintendo without even breaking a sweat.

I dont think there is any chance

That is a wonderful list of features and applications. Most of them are also available on PlayStation Vita and 3DS either built in, or via the web browsers. Both of those devices handle many of those functions better thanks to the physical controls. No matter, how we look at it, when the only input method on a device is a multitouch screen, it is going to be limited. Sure, you can hook up other things like a controller, a mouse, a keyboard, etc. to the smartphone, but that doesn't help on a day to day bases. It is not a good deal, if you have to carry extra crap to get your device to do what you want.

The handheld form factor may not be the best for mobile needs in todays world, but it is by far a better design than the current slab phones. I can not wait for this era in electronics to pass, as we have hit a major wall in progress. Hopefully, it won't be much longer before people start getting fed up with the same device coming out every year with absolutly no improvements. Time to shake off the starts, and wipe away the cobwebs.

I just feel like I should also mention that I was totally sucked into the whole slab phone thing as well. I was absolutly livid when the 3DS, and the Vita came out. You can go back in my post history to late 2011 - 2013 and see for yourselfs. At the time I was touting much of the same things I see from others now. Then for a while I completely ignored Vita and 3DS. It was not until late last year that I finally woke up, and realized the reality of the current mobile situation. I started to use my 3G Vita as my smartphone in January, and sold off my Xperia Z3 after only having it about 4 months. I was using my Z3, and my Z before it, and my Xperia Play before that, for nearly everything you mentioned above. Now I do it all with my Vita, and I see the ignorance of my last several years.

I'm not sure about Nintendo focusing on the Handheld market. I don't think a dedicated game device can compete with mobile phones anymore. That's way the fusion idea kind make sense. Nintendo doesn't need to sell as much consoles as Sony. What they need is to have a profit. I hope their mobile games can also be successful in order to help them maintain their console business. 

This gen is on pace to finish at around

72-75 million - 3DS

15-17 million - Wii U

I wouldn't count on a home version of the NX coming close to the portable version's sales.