Nintendo seems to struggle with third parties for 2 huge reasons.
1) Their hardware has been outdated by the time it released on the last 2 consoles (Wii & Wii U). So while developers/publishers are putting games on PC, PS4, XB1 they don't want to have to make a separate version for the Wii U. Not only is it somewhat expected to have unique gamepad/motion control features, it's also going to be a scaledback/gimped port that can't perform the same as the other versions due to the console's weak hardware. No publisher is going to waste their money on making a lesser version of their game for a console that is not the #1 console, and with a "#1 console" like the Wii it's still not a guarantee. Gamers usually want the "best" version available, console gamers tend to ignore PC as the "best" and it becomes a battle between MS/Sony's versions, which are nearly identical, while Nintendo's is a generation behind...plus lacks solid online support. This is a huge reason why Nintendo doesn't get the 3rd party support. Not because of their burned bridges in the 90's.
2) The second reason Nintendo struggles with third parties is because Nintendo keeps them in the dark about their new/upcoming consoles. Outside of a couple publishers aiming for a launch title, Nintendo generally doesn't let them know there is a 3D/Motion/GamePad/Touchscreen feature tied to their new system. They don't want word to spread and have the competition (Microsoft/Sony) steal this, announce it first, and put it in consumers hands at the same time or before Nintendo. I don't really blame them for this when you consider almost every Nintendo "gimmick" or innovation has been copied by the competitors in some form or another, but it really hurts them by keeping third parties in the dark. This basically created a "wait and see" approach for the publishers to wait and see how successful Nintendo's new console is before they dedicate any resources to building a game on it (which will require a more complicated porting process than PC/PS4/XB1). But this also hurts Nintendo because they miss out on a bunch of games at launch, and the lack of third party titles make consumers less hesitant to pick up the new console. With the Wii U in particular, some of the third party titles had already been on the 360/PS3 for a year, or were releasing at the same time. The Wii U versions were offering nothing new to them that would warrant the purchase of a system that was doing exactly what consumer's 360/PS3 was already doing. This all resulted in the Publishers waiting longer for the system to succeed, and eventually writing it off, finding it not worth porting games too.