NES - 62 million
SNES - 49 million
N64 - 33 million
Gamecube - 22 million
This is why after the Gamecube back in 2005, Nintendo couldn't afford to make an HD system. Yeah they still made some profit off the Gamecube but the overwelming majority of their money that gen came from the GBA. After a clear drop in every home console they released since the NES, there was a clear concern Nintendo's home console market would soon be dead. That's why they decided to change things up with the Wii but made the system weaker so if it failed it wouldn't damage the bank.
Once again, nobody had any idea how popular the Wii would become. Do you not remember all the conversations in 2005 after the Wiimote was first revealed how risky everyone thought it was? Even Nintendo was shocked by its success which is why Wii were so hard to find its early months because they had no idea demand would be so high. Had the system been comparable to the 360/PS3 in power and sold less then the Gamecube, it would have cost Nintendo billions. Making the system a modified Gamecube like they did wouldn't have seriously hurt the company if it failed since it was much cheaper to produce.
It's easy to say now how Nintendo could have made a more powerful console but nobody could have predicted its success back in 2005.
The Xbox 1 sold 24 million which isn't much more than the Gamecube and they went all in on the HD era and did extremely well.
I think my problem with your analysis is we've gone round and round with why Nintendo has been unsuccessful. I've often maintained that third parties and lack of standard features (online, optical, etc) are the reason that Nintendo loses Marketshare, not some cost that is too high of a price. In fact, Gamecube era is really the start of Nintendo's cheaper is better approach to the market (coming at $200, when the competitors were at $300) and it did nothing for Nintendo from a market prospective except convince the market that the Gamecube hardware must in fact be inferior.
I know that Gamecube was > in power than a PS2, but I was in college then and it was amazing the perception that it was in fact less powerful than a PS2.
The Wii was more successful than most imagined, but it was largely due to a gimmick or at least unique feature in motion controls. The problem with selling because you're innovative is that you have to constantly innovate and nobody knows for sure what is going to catch the market. Wii U was an attempt to innovate (touchscreen) and it has failed to capture the market the way the Wii has. The fall back then is what Nintendo has always done well. Create good first party games. But this has become less of an emphasis for Nintendo because they (since the Wii) have been used to selling a console based on features rather than games.
Nintendo is in the same market as Sony/Microsoft despite them pretending they are not. They should have matched the standard market feature of HD. It hurt Nintendo doubly because now they have to rely on first party games and they are having the HD growing pains that developers had 8 years ago and are having a hard time bringing games to market.
Every reason you listed would have been a reason to keep HD out of the Wii U. Much like the Wii, nobody knew if the console would capture the market, it hasn't yet. Nintendo needs to focus on the market and what the market needs and that will take care of the declining marketshare. Unfortunately Nintendo likes to think they are a market of themselves and that people will buy them in spite of their decisions.