I actually don't think third parties will have all that much to do with the success or failure of the Switch. When Nintendo systems do well, it's typically on the strength of their own games, and when they fail it's typically on their first party catalog either being too small or too weak. The 3DS may have gotten a price cut, but it was releasing a game consumers actually wanted that gave it a kick in the seat of the pants. Nintendo fusing their game streams together is a tactic intended to supply that properly.
I've already said why I think Nintendo is limiting Switch supply, but if it's really so demanded then I imagine them increasing the supply accordingly. Remember, the amount they're making for the fiscal year is likely for a two week span, not for the several months that less than twice this amount is usually intended for and doesn't even sell out with. Everyone assumes Nintendo has an insidious plan to deny them their stuff, but at the very least historically and with their recent attitudes blinking through their personas at moments it seems like there's other reasons contributing.
I think the Switch's success or failure lies more in the hands of how many different first and second party games people actually want there are and their marketing department than what personally incenses a handful of gamers on a forum. What's leaked about the former and what has happened with the latter are far better signs than the Wii U so far, but at the end of the day Nintendo's fate either way is far from determined.