Let me take you through what I see happening had Nintendo released a $400 PS4 rivaling Wii U.
The console launches in 2012, but doesn't have a launch title at all. NSMBU is still being worked on because they now have to get it up to PS4 quality graphics. NSMBU finally launches in May 2013. Pikmin 3 and 3D World are also delayed by 6-8 months for the same reason. Ditto for any 2014 Wii U exclusives.
Dragon Age Inquisition, Shadow of Mordor, GTAV, Diablo 3, DMC, Bioshock Infinite, Tomb Raider, etc. all skip the powered up Wii U leaving it to languish with almost no games for all of 2012, 2013, and 2014. "But how do you know these games would have skipped a powered up Wii U?" Because they were all on PS3, and skipped the regular Wii U.
To top it off a powered up Wii U likely would have still been 3rd place in the horsepower rankings because it launched a year earlier.
So here we are summer of 2014 and this PS4 rivaling Wii U has NSMBU, 3D World, Pikmin 3, and that's it. DKC, Mario Kart, and Bayonetta have all been delayed to the holidays. Most of the 3rd party games just outright ignored it. Why? Because making these games for a Nintendo console was never planned. Just like how 3rd parties got caught with their pants down from the Switch's success and took a couple years to fully support the system, this version of Wii U would have caught devs off guard as well. Except it wouldn't have had good sales like the Switch. It would have had bad sales. Worse than the regular Wii U. Because it would have had even less games than the regular Wii U! It would have been even more of a dumpsterfire than the regular Wii U!
How does a better console that is only 50 dollars more sell worst than the Wii U? Third parties were caught with their pants down with the Wii U. A Machine with with a worse CPU than the 7 year old 360. A system with similar architecture to the PS4 and Xbox One wouldn't have presented those problems.
The Wii U was a mistake in its entirety, but the lack of power hurt it as did other factors that is one of my points. Nintendo hoped to pull off a similar trick with it, but the casuals that the Wii attracted weren't going to fall for a 350 dollar machine that most didn't know much about.
The proof? Look at the numbers, 13 million units, a sharp drop from the 101 million units the Wii sold. The core and habitual gamers had made a shift to Sony and Microsoft.
The Switch has made a nice push in getting that market back because of portability and some awesome first party titles. But everyone that I know that owns a switch also owns a PS4. The Switch is really a successor to the 3DS as most people I knew that had a 3DS also owned a 360 or a PS3 in those days. The Wii U failed to grab those gamers back.
How does a better console that is only 50 dollars more sell worst than the Wii U?
The same way the Vita sold worse than the 3DS despite being $250, when the 3DS was $250, and $200, when the 3DS XL was $200. That's what happens when a system has no games.
Third parties were caught with their pants down with the Wii U. A Machine with with a worse CPU than the 7 year old 360. A system with similar architecture to the PS4 and Xbox One wouldn't have presented those problems.
The problem there is assuming that our hypothetical powerful Wii U would have gone with a similar architecture to the PS4. It wouldn't have, because it would have launched a year earlier, and Nintendo never does what everybody else does.
Also, Wii U was capable of 3 instructions per clock, and had 2 GB of ram. 360 was 2 instructions per clock and 512 MB of ram. Wii U didn't need such a fast CPU because it wasn't constantly grabbing info from the HDD like the 360 was.
I agree with the rest of your post, except for the following part...
But everyone that I know that owns a switch also owns a PS4.
Everyone I knew that owned a Wii also owned a 360 or a PS3. So Switch should be considered the successor to the Wii then right?