The reason the Wii and Wii U suffer from lacking 3rd party support is because developers find the hardware lacking compared to Xbox and PlayStation.
As for good games having to compete with bad games, that was also the case with PS2. That console had everything, good or bad. And tons of it.

And I don't think their main image problem has so much to do with how they catered for casual gamers, but rather the "for children" brand they've never been able to shake off.