Here's the thing, I understand your logic but it's flawed. For instance... every Playstation has had 10 or more years of shelf life. That doesn't mean each console was foggy on which gen it was a part of.
PS1 - 1995- 2005
PS2 - 2000 - 2014 <-- shocking
PS3 - 2006 - 2020 <-- also shocking
PS4 - 2013 - 20?? <-- still going
PS5 - 2020 - 20??
Regardless of overlap, we all agree what generation each Playstation is a part of.
For Nintendo, they were forced to cut the lifespan of the Wii-U short due to horrible sales. For all intents and purposes, the Wii-U was looking like their Dreamcast. They had to think quick and thus, they started R&D on the Switch quickly as a successor to not share Sega's fate. Luckily for Nintendo as well as the rest of us, combining their home and handheld markets into the Switch paid off and it became widely successful.
As for Switch technologically being a last gen machine, we can all agree on that but Nintendo opted after Gamecube to focus less on hardware specs and more on different ways to play. Thus, starting with the Wii, they were always technologically a generation behind their competition.