Mario Kart8 though. Most will probably move on, see no reason not too.

Champions of Norrath,  Champions Return to Arms, and many others are still playable online on the PS2.  The original Xbox online wasn't shut down until four and a half years after the release of the 360.  This is one and a half years after the Wii U released.  Three years and a few months after the 3DS released.  It's even a bigger issue with the Wii and DS because that's 250 million users compared to the 24million Xbox users.  With 400% more sales, the Wii servers should have stayed up until 16 years after the release of the Wii U to be comparitive to the Xbox sales/years servers stayed online. 

If Nintendo wanted to force people to move onto the next consoles and get Mario Kart 7 and Mario Kart 8, then they don't need to shut down the entire service.  There are still games on the DS and Wii that people play and no equivelant of these games on either the 3DS or the Wii U.

Well, I don't think MK8 will be as hackable as MK Wii, so there's your reason.

From what I gathered only private servers were up on the PS2 anymore, is that the case here?

We both know that only a small number of those 250 million users play online on a regular basis.

That's how I see it.  Why get a Wii U when you can get a Wii and play Mario Kart online?  Well, unless you were a sucker and bought a Wii Mini. 

I wouldn't be surprised if MK servers got the most traffic out of everything.

Me neither. Next to that is most probably Super Smash Bros. Brawl. That game has some neat multiplayer hacks as well but mainly just a very popular online Wii game.

I tried playing Brawl online once. It was shit.

Doesn't affect me at all, never owned a Wii or DS.