Back when Nintendo had a stranglehold on the industry, they put in place a bunch of anti-competitive policies in order to keep a monopoly in North America. Basically, third-parties got shafted all the way around.
Nintendo made developers agree to exclusivity just to have a game on a Nintendo system. I don't mean just exclusive games, I mean Nintendo demanded that developers release nothing at all on rival systems for a certain window. They made studios pay them to manufacture the cartridges but controlled production amounts, which ended up with third-party games always being under-shipped and sold-out during key retail periods. They demanded that developers make a working game first, without any agreement, then they would decided if they'd allow it on the system based on their own rules--for example, they might decide your game was too much like something they were releasing, which means you were screwed over something you might have gone into debt to make.
I remember one of the guys from EA saying they'd decided to become a PC developer rather than play by Nintendo's rules. Sega tried Nintendo's approach before opening things up for third-parties and then Playstation came and blew the doors off Nintendo's monopoly. Third-parties jumped ship because of practical reasons, like the CD format, but they weren't exactly sad about the turn of events.
What does that have to do with anything now? Business is business, after all. Executives don't stay at the top by holding grudges above profit margins.
In short, Nintendo created a situation where the third-party environment moved on to somewhere else. Their policies and hardware mistakes resulted in a divided market. I'm sure they thought that just being Nintendo would be enough to crush the competition and the third-parties would crawl back meekly but, obviously, that didn't happen. Moreover, the longer that didn't happen, the more the market fragmented.
At present, in my opinion, publishers are just fine with keeping things the way they are. Instead of releasing on four platforms, with the related increase in marketing, production, and distribution costs, they can release on three platforms with pretty much the same number of sales. There really is no reason for them to try all that hard to expand their existing framework unless it develops on its own.
If the Switch is a big success that steals away consumers from Xbox/Playstation/PC then third-parties will be there. If not, they're fine with ignoring Nintendo, too.
So, ultimately, Nintendo bears the most responsibility for the current situation with third-party developers and publishers.