Depends on the capabilities of the hardware.
-Continues to get dedicated Japanese support inherited from the 3DS (Monster Hunter, ATLUS titles, and maybe encroaching on the Vita/PS4 audience with stuff like God Eater or something).
-Maybe a portable bastion for some independent titles.
-Western third parties will continue to ignore it for the most part save for a handful of ports early on. The easy-to-exploit shovelware audience is mainly on phones, though there's plenty of trash downloadable software on the eShop.
If that thing is even less capable than an Xbox One, you'll have a hard fucking time to convince third parties to optimize for the Switch when Sony and Microsoft are hoping devs will transition upwards with the Scorpio and Pro. The Switch would have to be some monumental success that wildly outclasses the other systems...
Until proven otherwise, there's no reason to suspect this to be any different from Nintendo's previous hardware in that, beyond some notable exceptions, you're getting this for Nintendo's own software.