3rd partys are vital to the existence of a console. You just need important multi platform games like Far Cry 4, No Man's Sky, Skyrim and GTA to be relevant to the market.
3rd party's are not biased against Nintendo. They just had to learn by loosing a lot of money, that it is much harder to make any profit with the tiny user base and very strong 1st party competition.
Thankfully, the design is close to the Xbox 360 so ports are easy to make once you find ways to compensate the weaker CPU with the stronger GPU.
Nintendo needs to find creative ways ways to get all important 3rd partys full on board, even if it means reducing or even cutting license fees to reduce development risk or investing in 3rdd party publishers by buying a portion of the shares.