It sold insane amount of 1st party software, it did not sell nearly as much 3rd party software and most traditional multiplat releases did not do very well at all, it also did not show impressive software numbers for a market leader or relative to installed base, especially when compared to the 360 (which is suspiciously absent in a few points in the OP).
The Wii sold a lot of software. It did not do very well with tradtional 3rd party games, it has a significantly poorer tie ratio than both competitors despite having several 10 million selling titles and even a few 20 million selling.
It did not "fail at selling software" but it largely succeeded in selling 1st party and more casual oriented titles, 14 of its top 20 titles are Nintendo published and/or developed and make up about 1/3 of the total software sales on the platform, all of which is totally fine, but let's not pretend that it comes close to 360 or PS3 in 3rd party fare.