I think it would have gotten even less third party support that way, counter intuitively. If it was just Nintendo with their feet in next gen for the next 1-3 years, no way would they get support in that time, which is crucial for building the audience which will buy games for the rest of the console's life. Look at the Wii, early on, multiple million selling games across many different series and genres. But as they were just experimental games and never captalized on, it sort of metastasized to the point where the Wii wouldn't support third party games like those anymore.
If the Wii U got absolutely no third party games until the next PS and Xbox, it's software sales would be dead in the water, for its entire life. Nobody would want to triple their dev budgets just to make a Wii U game when the others aren't even out yet. At least this way, out of the gate Nintendo is going after the gamers who like Arkham City et al. So there's going to be a hunger for those kinds of games, which is good. Naturally, the downside is if third parties move past the Wii U in a year or two to support the next PS and Xbox.
But if these were the only two factors (they aren't, of course), I'd say Nintendo made the correct decision. It's not the one I, or indeed most sane gamers, wanted necessarily, but in terms of building an install base hungry for the types of games the Wii missed out on, Nintendo's on the right track.
