I think people often forget that generations are entirely arbitrary categorizations used in the industry to divide the history of console sales and competition into periods dominated by sets of hardware that were considered contemparies of one another and were each other's principle competition. The Switch makes the most sense as a Gen 8 platform. Yes, that means Nintendo had 2. Doesn't really matter. Barring miraculous legs or a surprise early launch for gen 9, the Switch will garner the majority of its sales in competition with the PS4 and Xbone. And it will do so over a period of 3 years or more. Rolling it into gen 9 would make no sense.
Absolutely correct. And having 2 consoles in the same generation is not unprecedented. Magnavox had 2 consoles in the first generation, Atari had 2 in the second generation, Sega and Atari both had 2 in the 3rd generation and SNK had 2 in the fourth generation. It's less common now but it's certainly not something unique to Nintendo this generation.
Too many people think power determines their inclusion into a generation but nobody in the industry itself has ever used that criterion.
The video game crash counts as a separate generation. That explains why it "appears" that some of those consoles were in the same generation. Truth is that Atari 2600, 5200 and 7800 were all in a different generation. Each one was meant to be the successor to the previous one. But Atari 5200 was the console of the "crash generation" so it incorrectly gets lumped in with generation 2.
The second situation where it seems like their are 2 consoles in the same generation is when their are two product lines. Like we could say Nintendo had the SNES and Gameboy in the same generation, but those are obviously two different product lines. So you could also have Atari ST and Atari 7800 released close together, but those are also two different product lines.
The third situation is when a console is canceled prematurely after 1-2 years, like the Virtual Boy or the Sega SG-1000. In this case you can have two consoles in the same generation, because the first one was canceled very prematurely. On the other hand Switch was released 6 years after 3DS. That is a normal generation. Switch was also released about 4.5 years after the Wii U. That also is normal for a generation. Historically, 4-7 years is the normal time frame for a generation.
Bottom line is that Switch is in the next generation. The term is not an arbitrary construct. A typical console grows, peaks, declines, and then spawns a successor while continuing to decline. This repeated pattern is very analogous to a that of a living organism (or group of organisms) so it is called a "console generation". It's a simple way to describe a set of complex phenomena. People use the term generation, so they can make sense of it all. And originally the term was used to simply tell customers, "hey guys we have another console coming out." By any reasonable definition of a console generation, the Switch is generation 9.