You're supposed to play on a CRT, then the dithering won't be so noticable.

I noticed it particularly in Mario Odyssey although I think it was a stylistic choice, still it'd be interesting to know if it really is or what.

I also suggest you use another Xenoblade 2 picture because spoilers

The best example was that screen. It's heavily censored.  I already said that in the OP. You drawing more attention to it with all caps makes it worse btw.

The Switch is two Saturns duct-taped together. But because it's a hybrid, one of the Saturns is a rocket from the 1950s.

I think its a choice in regard to low overhead shadow options.

I just remembered Street Fighter V on PS4 has dithering it and it looks bad because its on the characters.

I notice on Doom for X1 you see mesh patterns as you move but it seems to blend as you stand still. These are both games aiming for 60 fps.

In the case of SF II, for example, is simply because back then there wasn't any other way to do proper transparency. The "new" game still uses the same engine, just with higher quality sprites.

It's just an easy performance win. 

As a game with open non-linear worlds running at 60fps, Odyssey has to make cutbacks to look as pretty as it does, and the devs just decided that using dithered transparencies was a less jarring tradeoff than, say, lowering the screen resolution.

It's not like this technique hasn't been seen on the Saturn; plenty of Wii U, PS3, and 360 games used dithering as a shortcut. Take a closer look at the foliage in Battlefield Bad Company 2, to use an example off the top of my head:

This effect is very common in games, it is not something which was just used on the Saturn and now the Switch..

Probably as the ps4 and xbox one get to the end of their reign and the last games are released of the latest and best pc games conversions we will see more of this. I doubt many will care as long as they can play the latest and greatest games on their more humble hardware.

Nier: Automata on PC.