Futurama

Pretty much the only animated show that does real time commentary is south park and that is because their art style is "intentionally shitty" to allow for rapid turnaround... and even they have mostly shifted to trying to have a lot of episodes in the can. The rest tend to operate on often times an almost one year delay. And it is the same reason video games usually reference memes from three or four years before release.

Which, again, was the same with theatre. Sure there were playwrights who would make edits to scripts the morning of to reflect what the royal nonce was doing. Same as there are today. But it was always minor tweaks because you need to make sure your actors can learn their lines. The vast majority was written weeks, if not months, prior.

As for changing social values: Again, that is any media you look at. I recently rewatched The Venture Bros in preparation for the finale and was amused at how ridiculously racist, ableist, and homophobic the first season was... and that they were still using ableist slurs as of the last one (which, to be fair, was like 4 years ago). But, at the same time, being gay stopped being a joke and more just became a thing (except Shore Leave who is a treasure and more a joke about camp gay than just being gay... and is a straight up badass). And while 2/3 (probably 3/3 but she never has enough screen time) of them are complete monsters, it is kind of sweet that Action Man, Sean Connery, and Billy's Mom are heavily implied to have become a throuple with no jokes made about it at all.

You can see the same with The Simpsons in terms of what gags they think are safe or not. And even Family Guy and South Park in terms of what gags they think are "edgy" and not.

As an aside. The fantasy trope of "we need to put on a play to start a war or find our friend" maps much more to modern improv or even stand up comedy than theatre. The cliche talking puppets is basically The Daily Show or even Last Week Tonight. But having Dandelion get on stage and say "So what's the deal with airline food?"... would actually have been amazing. What was my point again?