I would hesitate to say yes, so I voted no.

I don't think generations are dead, but with PS4Pro coming next month and Scorpio next year, Switch clearly won't be competing with a truly new generation of hardware for a long time.

With Dreamcast, you had a system announced and launched just a few years before PS2, and had it survived it would have competed with Gamecube and Xbox for several years as well. There was a clear break between Saturn and Dreamcast as well. Until the seventh generation, it wasn't uncommon for the fist console in a new generation to launch several years before other more mainstream efforts. TurboGrafx 16 launch a year ahead of the Genesis and two years ahead of the Megadrive. The first 32 bit consoles were released a year and a half ahead of Saturn and PS1, and several years ahead of N64. Etc.

But Switch will be competing with an upgraded Xbox One and PS4, and will probably be doing so for most of the standard 5-6 year lifespan consoles tend to enjoy. I would, if anything, called it an 8.5 generation console, same as PS4Pro and Scorpio. Although for all we know, generations may truly be dead now.

I addressed this problem in my OP. VGC won't let me for some reason otherwise I would of edited it

I mean, they all are in their own generation. PS4 is Sony's fourth generation console, while Xbox one is Microsoft's 3rd gen console. That's not really something that only sprouted about because of the Switch.

why is this important at all?

 The same reason all categorizations are important; they help us have a shorthand when talking about things. If there is no consensus on that short hand, it creates an issue of affective communication.

If I say that, for example, that I hate Japanese games because they all have boring combat, you might be confused because of how varied combat can be in many different Japanese games and how "boring" the combat in some western games can be compared to Japanese games. If I then clarified that I don't like turn-based games, even if you don't agree, we at least have an agreed upon understanding for what I'm saying, what I'm including, and when I'm excluding.

This discussion of generations is important because we're stumbling upon a situation where some videogame consoles fit under a categorization where others eventually never will. It makes talking about game and timing in the same way difficult, if not impossible.

I'd say NS is in the same generation as Ps4 Pro and XboxOne S, probably 8.5

I view NS as an equivalent, since making a WiiU upgrade wouldn't make much difference and they are released during the same time span, more or less

could be gen 9 if the improvement is more noticeable than say, 3DS to new3DS or DS to DSi

It depends. Is Switch really Nintendo's next generation of hardware? To be honest, it looks like an upgraded Wii-U, i.e. the same difference there is between PS4 and PS4 Pro.

I don't have much to add LOL I agree with most of what you're saying. Very well put.

PS4 and Pro, X1 and Scorpio will run the same game between then, NS and WiiU won't so they have a generation separation while the others don't.

You buy a single PS4 or X1 game and run on both systems and the system will show the image that they can, so there aren't a proper generation difference so you can say they are 8.5 (same as DS to DSi and 3DS to N3DS) but on WiiU to NS you are going from 8th to 9th (or on nintendo mind going from their 6th to 7th generation)