The only way Nintendo pulls full third-party support back into their ecosystem is to create a favorable environment for that market, one that can't be ignored.
As it stands right now, publishers like EA and Ubisoft have very little reason to put all their products on Nintendo platforms. Why would they? They already have three platforms to worry about. Why develop a fourth platform and split development and marketing costs even further? The more cost efficient method would be to consolidate your audiences as much as possible--or, at least, use the existing consolidation to your advantage.
So, really, "third-parties" as a generalized group have little reason to alter the situation.
That means Nintendo would have to take the initiative. It's their platform and their responsibility. Of course, that would take a lot of time and money. They'd have to carve that market out by either developing games that are similar to those on other systems, by buying third-party exclusives, by contracting third-parties to develop first-party games, or by a combination of those methods. If they created a demand, supply would eventually fill that void.
I don't see Nintendo going that far, though. Rather, I think they're more interested in replicating the success third-parties have had in other genres with their own first-party work. That way they can have things like "shooters" and "fighting games" on their system while making all the profit on the software.
