Gamecube was also power competitive, had a price advantage, and got multiplats. None of that saved it from selling 22 million lifetime. I don't see any reason why a HD successor wouldn't sell similarly.
360 had key advantages over the Xbox that made it sell better, (the explosion of online play, appealing to lost Playstation customers) I'm not giving Wii HD any significant advantages GameCube didn't have, in fact I'm giving it less by inserting the delays and subsequent droughts caused by adapting to HD development.
Why wouldn't a Wii HD appeal to lost Playstation customers? It's a cheaper HD console. Why do they automatically have to go to XBox360? The whole premise is that Nintendo hardware is no longer a generation behind. We are still assuming PS3 was a big fumble at launch right? PS3 would still be $500/$600 at launch right? Those lost customers would get XBox360 if they prefer FPS games like Halo and they'd go to Wii HD if they preferred adventure games like Mario Galaxy and Twilight Princess.
Also, here is why Generation 6 is different from Generation 7. The PS2 had almost all of the games. After a quick internet search I found these results for the physical game libraries.
PS2 had far more games than XBox or Gamecube. This is why PS2 can sell far better than either one, even if Gamecube is a cheaper price. Price still matters but game library matters more. Now look at Generation 7. PS3 and XBox360 have close to the same number of titles. PS3 actually does have about 250-ish more titles, but XBox360 was usually cheaper to purchase. When the libraries are that close then price matters a lot.
Since XBox360 was getting a similar number of titles to PS3, then why wouldn't a Wii HD as well? Making multiplatform games became the norm in generation 7. If there is a Nintendo console with similar HD specs, then why wouldn't it get a lot of these ports too? A Wii HD would be very similar to the XBox360 in that it would be a lot cheaper than the PS3 and have a comparable number of games, because of multiplats. Now add in the Virtual Console and Wii HD becomes a decently viable platform. It would be competitive to both the PS3 and XBox360.