As a Nintendo fan myself, I have no problem with Nintendo going third party. I've never owned a rival console but the prospect of Nintendo games on hardware capable of superior graphics and online infrastructure is really appealing and exciting to me. On top of that, I would finally get the chance to try out some third party games that aren't available on Nintendo consoles without the huge cost of buying a new console to do so. It seems like consumers would benefit from Nintendo as a third party publisher.
In terms of Nintendo as a company, they would definitely benefit from access to a far larger userbase. If Knack can outsell Mario 3D World, it shows that Nintendo aren't reaching a wide enough audience to maximise revenue at the moment. In the long term, the value of the IP will diminish as well. The concept of Knack being more recognisable than Mario may seem laughable now, but if sales remain poor over the long term (5 year console cycle) it could eventually be reality.
The business would also be able to rid itself of the costs and risk associated with console production. The string of operating losses experienced by Nintendo are largely due to the performance of the Wii U, and removing this cost would definitely be beneficial and viewed favourably upon by shareholders. Being a console maker makes little sense when third parties aren't developing and selling units on your system as the platform royalty income can't compensate the cost of production.
Nintendo would also benefit from business relationships with Sony and/or Microsoft, if Sony are willing to pay for exclusive Ass Creed DLC imagine what they'd pay for 3D World exclusitivity. Sony/Mircsoft/Whoever may be willing to forego platform royalty to bring Nintendo software to their platform.
The main argument against going third party I constantly hear is "look at what happened to Sega." This is completely incomparable to the situation Nintendo finds itself in. When Sega went third party they were in financial ruin and had to completely restructure their entire workforce and lay off a lot of employees. The quality of their releases declined as a result of this. If Nintendo were to go third party their development teams wouldn't have to undergo such a massive turnover. They are in a financial position where EAD and other first party studios can carry on work as usual without letting anyone go.
The other thing I have heard before is that Nintendo EAD is able to create such masterpieces because they have such a large input into the design of the console and are involved in its creation. This is just patently false. The corporate structure of Nintendo has created quite a gap between hardware r&d and software development. We've had several senior developers and producers (most recently Aonuma) say they were unaware about much of the Wii U specs until only a few months before release.
So why are we so scared of Nintendo going third party?