Let's begin with some definition. Full, true third-party support entails having every publisher in this set onboard:
Sega (If they continue to make console games)
Konami (If they continue to make console games)
Every major system (every Xbox and Playstation system) has had this set of publishers. It requires that every one of these publishers makes games for the system and more than 80% of a publisher's console content should come to a system to qualify (everything multi-platform and non-exclusive title). Any other publishers/indie developers beyond that list is gravy - like NIS for Playstation systems.
Nintendo has not had true third party support since the SNES. Every system after the SNES has had some subset of the previous list, never the full list and if there was a time it ever had the full list, it did not include the full multi-platform library from that publisher in that era (when the Xboxes and Playstations did).
Let's face it. For those of you familiar with World of Warcraft, chew on this analogy - Nintendo is a casual guild trying to recruit hardcore players in order for them to participate in raids. I have tried that very thing. It is a near impossible feat. No matter how attractive Nintendo makes NX, they are beholden to the multi-platform publishers to support them. The publishers have no reason to support Nintendo. They have made their bed in Xbox/Playstation/PC. Nintendo is 100% risk to them.
Best case scenario was the Wii when Nintendo won the generation. The support from the major publishers was tepid at best and the games released for the system were the worst versions. Those publishers design their games with Xbox/Playstation/PC in mind and will continue to do so. Nothing Nintendo does now will change that.
Nintendo does not and will not have the development pipeline to make up for the lack of third-party support on NX. The only scenario I can envision for full, true third-party support of a Nintendo system is if NX where functionally identical to an Xbox One or a PS4 - so the publishers wouldn't have to spend much if anything for a port. Even then, I think it is still possible for the publishers to not support NX. In the mind of the some of these publishers, Nintendo doesn't even exist anymore.
Can we all agree the proper line up is
>PC (most games and you can use for work and other things)
>Xbone/PS4 (I can't really think of any major reason to pick one over the other but you do need to have one to play most AAA titles because PC ports are generally fucked)
>Wii U (if you had a childhood you had love for Big N)
>3DS (You don't play like a vita right? You have your PC to look up your animu and weird weeb porn)
let me fix it for you
>PC (tons of games of all variations, a lot of niche genres, decades worth of games)
>PS4 (ports of games your potato too slow to run, few niche games like Disgaea 5, EDF and such)
>Wii U (niche games like W101, Bayo, HW, X, and some N stuff if you are not sick of it or didn't grow up with it, screw region lock)
>3DS (a lot of handheld games, screw region lock)
>Vita (few handheld games, basically Disgaea/Dungeon Crawler/Muramasa machine)