The Wii has been a very polarizing system throughout its life. For every person who swears by the console, there were at least just as many who railed against it. One common complaint among the former, was that the system focused too heavily on "Casual games" instead of the "Hardcore" titles people wanted at the time. While that debate has mostly died down in recent years, in retrospect, I couldn't blame some people for thinking that way. What I think hurt the Wii's image in the long run, was the seemingly polar opposite views of the system between Nintendo Co. Ltd (Japan), and Nintendo of America.
To me, it always felt like NCL's vision for the Wii, and NoA's vision for it, became more and more detached from each other as the console's life cycle went on. In Japan, Nintendo maintained the belief that the Wii was for everyone, and continued to release games for it that appealed to a more serious audience such as with Disaster: Day of Crisis, Xenoblade, Pandora's Tower, Fatal Frame IV, Zengeki no Reglev, and The Last Story. Nintendo of America on the other hand, became more and more convinced that the Wii was primarily a family friendly system for big Nintendo franchises, and little else, leaving third parties to fend for themselves in the "Mature" space. According to Unseen 64, there were a number of Western developed "core" games in development that were cancelled by NoA as they didn't fit the "casual" oriented mold of games like Wii Fit. And those aforementioned "Core games" in Japan? Most of them never got a NA release.
Operation Rainfall in 2011 was a big sign that NoA and NCL clearly weren't on the same page regarding the Wii. Nintendo seemed to recognize that as well. In January 2013, shortly after the Wii U's launch, Satoru Iwata took over as CEO of Nintendo of America, replacing Tatsumi Kimishima, who was moved back to Japan to head up the HR and Finance departments.
I think if Kyoto and Redmond were able to find common ground more, then the image of the Wii wouldn't be as polarizing in the long term.