At some point, getting Nintendo would be a career moment and I honestly believe a good move for both companies. It's just taking a long time for Nintendo to see that their future exists off of their own hardware. A long time.... :-)
Also, less innovation. Nintendo, for better or worse, always does its own thing. Sometimes that turns out bad, but often it turns out interesting at least and amazing at best. PS and Xbox do mostly the same thing with small gimmicks that are sometimes just dropped (kinnect 2). Nintendo goes all out with stuff that nobody else does. Like the combined portable and home console, handheld with 3D, a console with a giant board controller, a console with nunchucks as controllers. It goes outside of the box boldly and people rightfully love it for it, even if their hardware is most of the times weaker than the other console makers.
I can't imagine that Xbox or Playstation would want to get rid of the business rival that deliberately not competes with them on the same level.