That's true, but it still won't be that easy unless the game has longer legs than the other MH games.

That's a good point.  PSP and 3DS have fairly similar lifetime sales.  PSP sold about 20m and 3DS a little under 25m in Japan.  They are also pretty close in sales worldwide too.  Switch sales in both Japan and worldwide are going to go clear past that.

The real question I would have is about the potential fanbase of Monster Hunter.  Like Pokemon seems to have around a solid 15m.  The DS and 3DS Pokemon games all sold around this amount even though the DS had about twice the install base.  On the other hand Sw/Sh seems to be selling better than all of those games.  I guess if even a disappointing Pokemon game can get a lift on the Switch, then MH probably will too.

5m now in 10 days meaning it moved another 1m in the following week.

Monster Hunter Rise has now shipped over 5+ million units

It shipped 4 million units it's opening weekend, which means it's already shipped and additional 1 million units over the last week.

Insane numbers for an exclusive game on only 1 platformhttps://t.co/Vrxflr6Gul

— Benji-Sales (@BenjiSales) April 5, 2021

https://www.capcom.co.jp/ir/english/news/html/e210405.html

10mil on the Switch alone is guaranteed.

I believe this already makes it the best selling Monster Hunter among those that were only released on a single platform.  Obviously, it still has a long way to go to get near MH World numbers.  However, after that Capcom has the next best selling MH at 4.9m, Monster Hunter Freedom 3 on PSP.
https://www.capcom.co.jp/ir/english/finance/million.html

Rise is definitely getting a lot of benefit from World's popularity.

And the Switch's. Two-punch combo for sure.

6m now.

https://www.monsterhunter.com/rise/us/topics/itempack/

over 10M, at best 12M for PC+switch.

What changed in World that made the series so popular in the West?

Quality graphics, good online multiplayer non reliant in local coop for the first time, released in both consoles and PC, less grinding nature, more accessible encounters, much less boring to play single player 

And good marketing and advertising, easier to get when you have a good partnership with Sony 

But to be fair, before asking why World become popular in West we need to ask why Monster Hunter was even popular in Japan in first place. You can pretty much say the game was a flop everywhere but Japan, so it's not like MH wasn't only popular in West it wasn't popular anywhere besides Japan 

I guess the very high number of handheld users in urban areas along with the tribal/Social mindset where you need to play whatever your friends are playing mitigated the lack of a good single player campaign, as such MH was before anything a social game

"World" isn't really a social game, at least not in the same way as previous installments. The lack of sales in Japan (compared to other entries) reflects that. 

Different selling points-> Different advertising for a different kind of customers -> Good Reviews and World of Mouth -> Good Sales