And Wii sold over 100m and Switch will sell over 100m. Then you consider the handheld market in the previous two generations and it's clear as day that PlayStation (and Xbox) aren't even remotely close to being the be all, end all in the console market. There is large demand for consoles that are not like PS and Xbox, and that's the expectation that the market has towards Nintendo and it has been proven time and time again.
With the Wii U at E3 2012, Nintendo spent more time on AAA third party games than their own games. As if the important thing would be to have the same games as PS and Xbox. Nintendo was very wrong, but that's part of the reason how the Gamepad came to be. Third parties wanted a dual analog controller and the hook that Nintendo came up with was not as commonly mistakingly believed to emulate tablets, but the revival of the failed multi-screen idea that existed on the GameCube with the GBA connectivity. That's why it's no coincidence that The Wind Waker was remastered (used the GBA link on the GC) and that Nintendo Land featured game ideas that were present in Pac-man Vs. (another GC game). The Wii U was intended to support more than one Gamepad, but that idea got shelved because it was already too much of a challenge to sell the console with one Gamepad.
I agree Nintendo shouldn't try to be a Playstation or an Xbox. The times they attempted, it didn't work out well for them.
Gamecube, many people don't remember, was seen as a kids version of PS2. PS2 junior, in other words. The Wii and the Switch have heavily differentiated themselves from the PS/Xbox market.
I wish I could find the discussion about Wii U's inspiration from Gamecube. I think it may have been Miyamoto who brought that up.
I describe myself as a little dose of toxic masculinity.