The last time a show did this was NHK

That’s a bit of strong statement, there is probably a bunch of shows doing it, maybe in smaller quantities. I haven’t seen this cat show but often when I see a clip (like this one) it reminds me of Gintama. Gintama kinda does the same thing you are describing. Also Sayonara Zetsubou Sensei comes to mind, but there they also just straight up say things out loud. There is probably a bunch of shows that we both don’t know. Of course Japan being a country with an indirect culture, it has its own way of critiquing things.

It’s no secret that Japanese society isn’t perfect, but like India, people that call it out are looked down upon.

Certainly in some countries this is more of thing like you say, but I think this is still kind of a thing in western countries with a culture of more direct critique. For example: I’m not an American but I have definitely seen the American right accuse the American left of hating America when they critique America.

But yea maybe I’ll give Yani Neko a try sometime.