Some additional franchises that I thought of:
SNES: Yoshi's Island (Yoshi's Story, Woolly World, Crafted World series)
N64: Pokemon Snap (N64, Switch), Pokemon Stadium (Coliseum)
Wii U: Super Mario Maker (this and Splatoon were major innovation from Nintendo, imo, during the Wii U era)
From a commercial success perspective, Pokemon has really been Nintendo's biggest new-IP find since the NES days. While this started on a handheld, the N64 was really the first home console that saw Pokemon games and it did get a lot of them and so I will give N64 the Pokemon prize for the purposes of this thread. Smash Bros is probably #3 on the list for new IPs in terms of popularity post-NES after Pokemon and Mario Kart and so I will have to say that the N64 is the overall winner here.
It's a tough question though because the SNES had so many franchises that started on the NES but rose to fame in a major way on the SNES (Mother, Final Fantasy, Metroid), it just seems unfair to give all the glory to the NES for these franchises.