I also think there is a false equivalence when discussing about third-parties support.
Of course, the best scenario for Nintendo would be to have full third-parties support, as it was during the NES/SNES days. Nevertheless, Nintendo has many strong franchises in Japan: Pokémon, Mario, Animal Crossing, Zelda, Kirby, Splatoon; in fact, some of them are the biggest IPs over there. Also, Nintendo is able to produce successful franchises quite often (Splatoon is a recent example, but think about Rhythm Heaven, Tomodachi Life, Pikmin).
This is a double-edged sword: first-party support can suck sales potential from third-party games; but when attractive enough, it might be able to drive hardware sales; after all, Switch is selling solely thanks to Nintendo support (the fact that it is an attractive product also helps; the counterfactual, though, is harder to imagine: would have the same hardware with PS4-like games succeeded?).
This is not to say that Nintendo does not need third-party support: quite the contrary. At the same time, it is quite established that it does not need third-party support as Sony does. Sony relies heavily on third-parties because its internal offering is not attractive in Japan. Of course, Sony has some successful IPs, but nothing comparable to the like of Pokémon and Mario, and to successful third-party franchises, such as Dragon Quest and Monster Hunter. Sony is really dependent on third-parties; we can say that the major factors to explain PS Vita failure was the lack of Monster Hunter (and consequently of many big third-parties IPs such as Final Fantasy, Metal Gear Solid and Kingdom Hearts). And third-parties are volatile; we saw this during the DS era, when everyone was expecting Dragon Quest to be announced on PS3, and instead the franchise found its home on the portable device.
We are also looking at the situation where Sony got 90% of the relevant third-party support, and still its hardware is failing to reach a mass-market status (in 2017, outside big releases, PS4 was struggling to maintain a weekly average 30k units sold; this after revisions, AAA games, promotions). On the other hand, Nintendo hardware shows how they can be successful without major third-part support; even the DS, the most successful hardware of all time in Japan, was lacking major entries in Final Fantasy, Kingdom Hearts and Monster Hunter franchises (because of technological reasons, but still), and some third-parties barely showed up (Capcom support was abysmal considering hardware sales, and companies such as Konami and Koei Tecmo released either low-profile or kid-oriented games).
Henceforth, I am not saying Nintendo should not improve its relationship with third-parties. Nevertheless, Nintendo does not need the same amount (or the same type) of third-party support Sony needs to succeed. Of course, the more the better, but it is necessary to consider Nintendo games in the big picture, which are successful, drive hardware sales, and per se are relevant support.