It depends what you mean by believed in.

I think it is (or at least was) a useful tool for categorizing things.  The way that at least Nintendo is doing business right now, I don't think it's useful anymore, at least in regards to their products.

What is the purpose of debating whether the Switch is a 9th or 8th generation system?  How does this improve our understanding of the market?  Does it help us to make predictions?

What I mean by "believed in" is that I think it is more than a system of categorizing things.  Console generations also help explain other things about console sales.  In this case it helps to explain which consoles are competing with one another and which ones aren't.  How does it help us make predictions?  Because sometimes consoles in the same generation don't launch in the same year.  But you still know they are competing if they are in the same generation.

Here's an example:
Go back to December 2005 in the US.  The XBox360 had just launched and sold 536k systems.  That same month the PS2 sold 610k systems.  The NPD this month probably would have reported PS2 as #1 and XBox360 as #2.  How do we interpret this data?

Person 1 thinks the PS2 and XBox360 are directly competing because they are home consoles selling at the same time.  To this person console generations are arbitrary.  Any system selling in the present is part of the current generation.  They might say something like, "Nothing can stop the PS2.  Microsoft releases a brand new HD system and the PS2 still wins.  XBox360 is dead on arrival.  It can't even beat the PS2.  Just wait and see how hard it gets clobbered by the PS3."

Person 2 thinks that PS2 and XBox360 do not compete, because the two systems are too different from each other.  They see the XBox360 as selling in a different market instead.  This person might say something like, "Both the PS2 and XBox360 sold really well this month.  They aren't competing with one another though.  The two systems are just too different from each other.  The XBox360 is in HD and has an internet service.  It can't possibly be competing with the PS2.  Two home consoles can be successful at the same time and this is the proof."

Person 3 thinks that the PS2 and XBox360 do not compete, because they are in different console generations.  They see the XBox360 as competing with the PS3 because they are in the same console generation (even though the PS3 hasn't been released yet).  They might say something like, "Why are we even comparing the PS2 and XBox360?  The PS2 already won Generation 6.  The XBox360 is a Generation 7 console.  The XBox360 is competing with the PS3.  They were really smart to release a year early because almost none of those 536k people who bought a 360 are going to get a PS3 too.  Sony needs to be careful with the PS3, because Microsoft has a 1 year head start on them."

So, we all know how this turned out.  The XBox360 actually competed with the PS3.  Microsoft took a lot of market share from Sony during Generation 7.  Person 3 was right all along.  This is obvious to us now, but it wouldn't have been obvious to a person in 2005.  The PS3 hadn't even released yet, so how could it be competing with XBox360 in 2005?  It's because they were going to be in the same generation all along.  The PS2 had already competed with the XBox and won.  The successor to the XBox, the 360, was always going to compete with the PS3, because it was the successor to the PS2.

Of course, I chose these examples because this is how I view the Switch and the PS5.  I could have also compared the PS2 and the DS.  In this case, person 2 would have been correct, because the home market and handheld market are actually different markets.  Person 1 is never correct though.  He believes that console generations are arbitrary.  This is incorrect.  Systems only compete when they are both in the same market AND the same generation.  More importantly, console generations are more than arbitrary categories, and they help us explain sales data and make accurate predictions.

This begs the question, "So is Person 2 or Person 3 right about the Switch?"  I have my reasons why I think Person 3 is right (and I could give them), but my post is already long enough.  My main point for explaining this is to talk about things on a simple level with a clear example.  A person has to crawl before they can walk.  We have to understand what's going on in the simple cases, before we can understand the complex ones.  Switch is a hybrid console.  That makes it complex.  If a person doesn't understand the simple cases, then they definitely aren't going to understand the Switch.  They also aren't going to be able to make accurate predictions. 

I hope I've made it clear that a console generation is more than just an arbitrary category.

For me a console generation is relevant to the technology and games (not exactly price or power). So if most of the multiplatform library of Switch is on PS4/X1 it is on the generation of both, if the library is more shared with PS5/XSX then it would be on the next for game. But on technology standpoint most of the tech on its inside is closer to PS4/X1 than it will be with PS5/XSX. So considering both points and that we are still going to have crossgen game by 2021 and even 2022, Most of its technology, library and time were on the 8th gen so it is a 8th gen system.

Generations are really more about launch timing than game library. 

But even still, do you think the multiplatform games are the main things driving sales on the Switch?  Is it Zelda, Smash and Animal Crossing driving sales?  Or is it Witcher 3, DOOM and DQ11?  People are mostly buying Switch for games they can't get anywhere else, and once they have the system then they might buy some ports too.

What I mean by "believed in" is that I think it is more than a system of categorizing things.  Console generations also help explain other things about console sales.  In this case it helps to explain which consoles are competing with one another and which ones aren't.  How does it help us make predictions?  Because sometimes consoles in the same generation don't launch in the same year.  But you still know they are competing if they are in the same generation.

Here's an example:
Go back to December 2005 in the US.  The XBox360 had just launched and sold 536k systems.  That same month the PS2 sold 610k systems.  The NPD this month probably would have reported PS2 as #1 and XBox360 as #2.  How do people interpret this data?

Person 1 thinks the PS2 and XBox360 are directly competing because they are home consoles selling at the same time.  To this person console generations are arbitrary.  Any system selling in the present is part of the current generation.  They might say something like, "Nothing can stop the PS2.  Microsoft releases a brand new HD system and the PS2 still wins.  XBox360 is dead on arrival.  It can't even beat the PS2.  Just wait and see how hard it gets clobbered by the PS3."

Person 2 thinks that PS2 and XBox360 do not compete, because the two systems are too different from each other.  They see the XBox360 as selling in a different market instead.  This person might say something like, "Both the PS2 and XBox360 sold really well this month.  They aren't competing with one another though.  The two systems are just too different from each other.  The XBox360 is in HD and has an internet service.  It can't possibly be competing with the PS2.  Two home consoles can be successful at the same time and this is the proof."

Person 3 thinks that the PS2 and XBox360 do not compete, because they are in different console generations.  They see the XBox360 as competing with the PS3 because they are in the same console generation (even though the PS3 hasn't been released yet).  They might say something like, "Why are we even comparing the PS2 and XBox360?  The PS2 already won Generation 6.  The XBox360 is a Generation 7 console.  The XBox360 is competing with the PS3.  They were really smart to release a year early because almost none of those 536k people who bought a 360 are going to get a PS3 too.  Sony needs to be careful with the PS3, because Microsoft has a 1 year head start on them."

So, we all know how this turned out.  The XBox360 actually competed with the PS3.  Microsoft took a lot of market share from Sony during Generation 7.  Person 3 was right all along.  This is obvious to us now, but it wouldn't have been obvious to a person in 2005.  The PS3 hadn't even released yet, so how could it be competing with XBox360 in 2005?  It's because they were going to be in the same generation all along.  The PS2 had already competed with the XBox and won.  The successor to the XBox, the 360, was always going to compete with the PS3, because it was the successor to the PS2.

Of course, I chose these examples because this is how I view the Switch and the PS5.  I could have also compared the PS2 and the DS.  In this case, person 2 would have been correct, because the home market and handheld market are actually different markets.  Person 1 is never correct though.  He believes that console generations are arbitrary.  This is incorrect.  Systems only compete when they are both in the same market AND the same generation.  More importantly, console generations are more than arbitrary categories, and they help us explain sales data and make accurate predictions.

This begs the question, "So is Person 2 or Person 3 right about the Switch?"  I have my reasons why I think Person 3 is right (and I could give them), but my post is already long enough.  My main point for explaining this is to talk about things on a simple level with a clear example.  A person has to crawl before they can walk.  We have to understand what's going on in the simple cases, before we can understand the complex ones.  Switch is a hybrid console.  That makes it complex.  If a person doesn't understand the simple cases, then they definitely aren't going to understand the Switch.  They also aren't going to be able to make accurate predictions. 

I hope I've made it clear that a console generation is more than just an arbitrary category.