When talking about the Wii, it is very crucial to keep in mind that Sony and Microsoft lost massive amounts of money with the PS3 and Xbox360, especially at the start of the generation. They literally lost billions of dollars and Nintendo could simply not afford a scenario in which the Wii was sold at a loss or even at a break-even price and then would go on to do Gamecube numbers.
We should also keep in mind that HD software development would've been too expensive and time consuming for Nintendo at that time.
In hindsight, a Wii for $299 with a better CPU (for example: 1 GHz instead of 729 MHz), higher GPU clock speed (say, 350 MHz instead of 243 MHz), more RAM (128 MB instead of 88 MB) and HDMI output for better picture clarity, in a slightly (!) larger form factor would've been a better idea. But we should keep in mind that the small size of the console was part of the marketing message. It was a clear differentiating factor for the console.
But in the early 2000s Nintendo was not in a position to gamble on profit margins, especially because they also had the DS competing against the PSP - and back then everyone expected the PSP to kill Nintendo's handheld business.
