Didn't Nintendo release an entire new generation of systems with almost no motion controls built on them after the Wii?

I'd say refined motion controls. I had a quite a few Wii U games that had motion controls but in a limited capacity. After playing games like Zelda and Splatoon, I miss the little extra precision when I play games on PS4 ( which has them and often doesn't use them!) and Xbox.

Maybe, but WiiU barely dealt with those motion controls. I think aside from the gyroscope for things like Zelda/Splatoon and the motion steering of Mario Kart, WiiU really stood away from motion controls. Same with the 3DS, which merely used the gyroscope for things like the built-in face shooter or Zelda, once again. That's two systems from Nintendo that clearly used motion controls in a very limited way (and hardly ever enforced it) and opted for a much more traditional scheme.

SuperChunk also uses examples like Breath of the Wild for the continued use of motion controls as a core concept. Motion controls are present on Playstation too, with games like Until Dawn, Second Son, The Last of Us (this one in a very limited way) and Flower using the Dualshock 4 in clever ways, and only using motion controls in games that make sense instead of being shoe-horned everywhere, as well. We also had a whole generation of streamers doing lewd things with the motions during the first year of Playstation 4 until Twitch banned it entirely.

Basically I'm disagreeing with both the notions that "it's a core functionality" as if that was continuated since the Wii (which the WiiU and 3DS clearly prove not), and that it's "non-existent" on the other consoles, when that isn't really the case. Sure, it isn't a priority either, but it's not like it is absent.

I haven't even seen a kinect sold in stores for over a year now.

No, no they didn't.

WiiU and Switch both build-on the WiiMote motion capability.

1. WiiU actually used Wiimotes as a primary controller plus gamepad has motion.

2. Switch joycons have an even more advanced motion than wiimotes.

There's also 3DS, which like I said had gyroscope but used in a very timely, almost non-existent way. 3DS and WiiU are the both systems I was alluding to (eight generation), which Nintendo almost entirely glossed over motion controls.

Also, Wiimotes as a primary controller for the WiiU is...not a good example by any stretch of the imagination. First of all because the system's primary controller is the Gamepad (you need the Gamepad for most things WiiU related, not to mention that not every WiiU game supported Wiimotes but all do support the gamepad) and I think this is basically something that can't be argued against, and second of all, because most of the games that did use the Wiimote as an auxiliar method for the gameplay did it without recurring to motion controls, but basically using the Wiimote as another standard controller, such as the case with New Super Mario Bos U or Smash Bros. 

WiiU gamepad does have motion controls, but like I replied to d21lewis, it only have very few examples like Splatoon, Zelda and probably something else I can't think of for its use. Motion controls on WiiU were barely non-existant, and hardly ever used at all. It wasn't a "core" feature of the system because it was barely utilized, it was just something extra implemented as a built-in. If Gamepad is somehow valid, so are the Dualshock 3 (EDIT: not necessarily, since it was only a specific sixasis model, but still) and 4 then, which also used motion controls and thus void your notion that it is "non-existent" in other systems.

Nintendoland, a launch 1st party game, required wiimotes and gamepad. Gamepad had a built-in sensor bar to marry itself to the wiimote. Clear examples that the Wii U was definitely launched with the notion that wiimote is a primary controller and with motion in mind. 

Plus, there are several games that use the motion functionality built-into the gamepad. ZombiU, Batman, Mario Kart, Nintendoland, etc. This implementation is the predecessor of what we see in Switch and its Pro Controller.

I was only considering consoles, not portables so I did not think of 3DS though it has limited motion as you noted.

awww I love turning off my xbox with voice commands. I wonder if the kinect will work with the next few systems still? to keep some functions.

They released the AIM controller which at least has dual analog sticks, yet the fundamental problem remains. A single camera (or actually 2 cameras close together) can't deal with occlusion. You either need two on either side or use a different form of tracking. Releasing new move controllers with analog sticks would at most be a temporary fix. And actually you can use the DS4 for that. The DS4 is tracked just as well by the camera and not that hard to hold in one hand. When you have 2x DS4 why bother with Move :/ Except no devs have figured that out yet...

Next gen needs a different tracking method, time to put the glowing balls to rest.

Get kids, it works too. They can even retrieve the controller for you. Kinect, your move :)