An HD Wii, or whatever it would have been, would have lagged severely behind the 360 and PS3. There were three major advantages that worked in the Wii's favor. 1) It was significantly cheaper than the competition. 2) It was innovating and captivating with its motion controls when it launched. 3, and most importantly in my book) It was easier and quicker for Nintendo to develop games for than if the architecture and hardware was on par with the 360 and PS3.
In this alternate history games like Super Mario Galaxy and Metroid Prime 3, while they would have been visually mind-blowing, some of the most beautiful looking games of their generation (which they are already in the case of Galaxy), those games would have turned out noticeably different than they were on the Wii, due to their motion controls. Most importantly, they would have taken much longer to develop for and release. So instead of Galaxy coming out in late 2007, it would have been pushed back to mid-late 2008. All of its major games would have come out later than they originally launched, which would have been a huge problem. Remember the Wii U and its software droughts? There you go.
Hardware Comparison Threads: