The only exception I can think of would be students writing essays as college papers. My son wrote a paper about the philosophical themes reflected in two Cohen Brothers' movies (No Country for Old Men and A Serious Man) as a requirement for his BA in Media Arts and Culture.
A lot of people still think of essays as school papers that start with "In this essay, I will blah blah blah" and end with "So in conclusion, blah blah blah" and in between cite a bunch of academic papers and research.
But I, and most people who are familiar with literary essays (like those in The New Yorker, for example) think of them as more creative and informal pieces that people read for information, entertainment and novel ideas. And it's hard to think of a publication that would run an essay about an old TV series or movie. It would have to be really, really good and say something strikingly new. And maybe not even then.
The only exception I can think of is someone writing something about a really old but widely familiar show. Someone not long ago wrote a piece on Slate "proving" that Mike and Carol Brady had killed their dead spouses. It was silly, of course. But someone on Facebook posted it who apparently knew the essay's writer. I wrote a comment with a link to that related New Yorker short story about the couple on the plane. The writer of the Slate essay popped in to point out that story contained no proof, whereas his essay was supported with "evidence."
He did have a point. One of his pieces of evidence, for example, was that in this big happy family made of bereaved widows and grief-stricken young children, nobody ever even mentions the deceased spouses/parents. Which would be really weird, come to think of it.
And I read another essay recently about how Ross and Rachel, the lovebirds of Friends who finally get together in the last episode, were actually a terrible couple and that Ross treated Rachel like shit. She made some valid points, also with evidence. I can't imagine anybody being interested except those who watched Friends (though admittedly, that's a lot of people, including me).
Whereas I never watched much of The Brady Bunch, but certainly have seen and heard enough about it to feel pretty familiar with the setup.
Oh now I can think of one more essay about TBB that I first read a long time ago, possibly even in the New Yorker. It was called "Here's the Story" in reference to the opening words of TBB's theme song, and he connected his regular TV watching in childhood and to the similarities and differences in his real life. That one was pretty good, too.