Sure, you can look at it from that perspective too. At least that way you would not consider Switch Nintendo's second gen 8 console. PS4 becomes a gen 4 console, Xbox One is gen 3.

The most widespread definition for generations is the one found on Wikipedia though. It's not perfect, because gen 1 is all the boxes that had built-in games and gen 2 are all the boxes that used modular games until the video game crash in the USA in 1983 happened. The NES is the beginnning of a new age, so that's where gen 3 starts off by modern definition.

It wasn't always that way, because writeups that date back to the early 1990s refer to the NES as gen 4. The Atari 5200 was part of the original gen 3, but eventually that got wiped from history because the original gen 3 had no successful system. Perhaps that was done to forget the dark era of 1983 and create an image that consoles have always been successful. Or maybe it's the doing of third parties who wanted to create an image of third parties being the lifeblood of consoles. In truth though, the video game crash was caused by third parties; they destroyed the market. Regardless of the reason, the original gen 3 became part of gen 2 and was supplanted by the NES and its competitors as the new gen 3.

Why is that in doubt? Switch is Nintendo's only generation 9 platform, so they will give it their all and also cut the price aggressively if that should be necessary. Switch is also in good position to take the lionshare of Japan's third party support. That's not going to happen immediately in 2017 because third parties are always cautious about putting their weight behind Nintendo platforms, but since Nintendo needs Switch to sell, they are going to make it sell; and that's how the third party support will come.