The Switch launched at the same price as the PS4 Slim. I don't expect them to charge over $400 either, though.
The Dreamcast launched 4 years after the Saturn (and 3 years before the Xbox and GC), yet no one considers it a 5th gen console.
The power jump from GameCube to Wii was much less substantial than Wii U to Switch, yet no one considers the Wii a 6th gen console.
To have most of the same games (it doesn't) like an actual Pro version, the Switch would have to play the exact same type of media as the Wii U, which it doesn't. "It has ports and remasters from the previous console" is actually a counter-argument for the Switch being part of the same generation.
The rules are being applied inconsistently, and it mostly has to do with some people not liking the idea of a weak tablet kicking off the next generation of hardware instead of 'real' consoles like PS and Xbox.