It's not fuckin' rocket science.
3DS stumbled out of the gate, as you say, because it's launch lineup SUCKED. There were ZERO "must have" titles to help sell the console. The price wasn't even the issue, and the price drop, while it absolutely helped sales, wasn't technically necessary. What really picked up sales, was the release of MK7, and Super Mario 3D Land. When those came out, 3DS finally had some "killer apps".
Wii U is a bit different. It didn't stumble RIGHT out of the gate. In fact it did well within it's launch window, selling close to 3 million units. It even had a rather robust launch lineup, one of the single biggest arrays of launch software in gaming history actually. BUT, one thing it kind of didn't have, was a "MUST HAVE" killer app. Nintendo Land simply wasn't as readily accessible and "for everyone" as Wii Sports had been. Nintendo tried, and they obviously thought NL would be that, but it just wasn't. NSMBU was a great game, and it still to this day has the highest attach rate of any game on the console. But it was hindered by Nintendo releasing it FAR too close to NSMB2 on 3DS. The enthusiasm for the game would have been much higher if Nintendo had release NSMB2 much further away from U than they did.
Wii U's real trouble started in the first half+ of 2013, when they published a grand total of ONE title themselves, Lego City (which is a great game), and third party support during that same period also became sparse. Third party support AT LAUNCH was very strong. But because many of those games didn't sell very well, some of those third parties, namely EA, stopped or lessened their support going forward. System sales suffered because of a lack of software released for much of 2013. THAT, along with poor/lack of advertising, was the main cause of Wii U's troubles. Things picked up late in the year, which reflected in Wii U selling around 1 million consoles in the last few months of 2013.
2014 is going BETTER, with two Nintendo retail releases in the first two months, Wii Fit U and DKCR2. But then there's the gap between March and late May, before MK8 comes out. There is still, unlike last year, a slow trickle of third party retail software releasing in those months, and support is certainly steadier than it was last year. BUT, the simple fact is, if Nintendo had managed to release MK8 on April 30th, instead of May 30th, at least perception wise, that might've made all the difference in the world, as far as there seeming like a major gap.
But, the undeniable fact is, that Mario Kart 8 IS a "must have", system selling type of killer app title, and it's release WILL help Wii U sales. It's not a question of IF it will help, only a question of how much. Will it help some, or a lot? And how will Nintendo follow MK8? Will they manage to have a stronger, steadier release lineup from June-December 2014? One would hope so, especially considering that games like Bayonetta 2, Yarn Yoshi, and even X surely should all be close to done, all of them having been in development for years.
So regardless of whatever blather is being talked about Nintendo's "arrogance", nothing has changed as far as the real issue behind Wii U's struggles. It hasn't had a single, MUST HAVE piece of software to push the system. It just hasn't. It's had many GOOD games. But even Super Mario 3D World, as good as it is, was hurt somewhat by the perception that "oh, it's just another 3D Land game". So it also wasn't the "killer app" Wii U needed. Mario Kart will be, there is no arguing that. It only remains to be seen how MUCH it will help, and if Nintendo can drive the momentum forward going forward.