First and foremost, selling over 65 million units of hardware in an underperforming gen is nothing to be sniffed at.
Secondly, they are now starting a mobile venture in which their IP will reach an audience that dwarfs that of console users.
Thirdly, Im sure that if it benefited Nintendo to give up hardware and go software only they would have done so by now. Having millions of games selling on their own hardware with 100% of the profits landing in the bank, is obviously the best thing for them. As seen this gen, even small install bases like Wii U still has insane software attach rates and I dont see it changing any time soon.

They gave up out of failure not choice.

All of them should be a warning where nintnendo is heading.  Following their stubborn foot steps.  Hardware sales will fall so low they wont even make money of software they will lose billions.  Will be forced to abandon hardware and will enter 3rd party from a weak standing.  

All failed as they were to broke to weather the transition, ninendo could easily pull it of now.  5 years from now if nx fails and new handleld severly underwhelms they may lack the capital to transition succesfully to 3rd party.

They could die just like all of those did.  

The real question should be is why "Nintendo shouldn't be a third-party" ? 

Their strongest asset which is first party IPs, are at their lowest right now ...

I expect Microsoft to go third party and ditch being a console platform first and probably the only one to do so. It would be a huge surprise to me if anyone else did.

I got a wiiu and this will be the last nintendo hardware i ever buy, the maybe 7/8 games are just not worth a console purchase.  

Sure if corporations were not ran by stubborn pridefull often stupid arrogant people, but they are.  See how Kodak fared.  

100 year old and went bankrupt in a blink of an eye almost.  

Then ther is IBM that abandonded what made them them dropped PCs long before anyone else and looked to the future, and is mega succesfull still around doing billions upon billions of business.   

As someone majoring in embedded systems design. Nintendo hardware is pretty damn amazing. Especially the SNES and Gamecube. But the MIPS-based N64 is really interesting as well.

My comment about SEGA was more of a general response to something that's been said many times whenever this topic has come up.

My biggest question regarding the consequences of Nintendo going third-party would be, what happens to the Nintendo faithful?

Right now, Nintendo has millions of fans who are basically a captive audience.  They identify strongly with the company.  Some of them have little exposure to other markets.  Some of them are "super-fans" who buy pretty much everything Nintendo produces, including toys.  What happens when this consumer group is suddenly out of the pond and into the ocean?  Will their interests become diluted with other games, genres, and experiences that weren't on the most recent Nintendo consoles?  Maybe they don't buy every Nintendo title like they used to, maybe they develop attachements to other publishers and developers.  I don't know.

On the other hand, Nintendo hasn't been doing a good job of creating new customers, which is really the life's blood of gaming.  Hardcore fans are great but they won't make up for a lack of growth.  Nintendo desperately needs to find a way to expand their fan base.  That's something they must accomplish if they want to stay in the console market.  I know Amiibo was a direct response to this problem but, so far, it hasn't quite been functioning as Nintendo wants.

Honestly, if I were in charge of Nintendo, I'd keep producing consoles as long as I could see a profit per unit at launch.  I'd try to make sure all the browser and mobile games in Japan were on all my consoles and I'd try to keep a hold on the family market in the rest of the world.  There is absolutely nothing wrong with being in "third place" in unit sales if you're turning a solid profit.

That piece of junk was best selling console of last gen.

Really!? I would love to play few Sony games, namely Uncharted and Last of Us, but I am not going to buy PS4 just for those 2-3 games. Pretty stupid thinking, dont you think!?

You want to play Nintendo games, buy Nintendo hardware, simple as that.

Did Nintendo franchises popularity skyrocket on Wii? 3D Mario, 2D Mario, Zelda, Metroid, Kirby, Donkey Kong, Fire Emblem, Animal Crossing, Paper Mario, Punch-Out, Excite, Sin & Punishment, Battalion Wars, Mario Sports, etc all had very modest boosts over NES/SNES/N64/GC sales despite having 40-80 million extra sales. The only title that saw truly massive growth over previous installments was Mario Kart.