You’re going to be posting for a long, long time then.
Challenge accepted!
I’m going to stop reading this thread now, good luck on your quest. By the way, the correct way to refer to a TV-series episode is “The one where ‘whatever bit you actually remember from that episode’ happened”.
I asked this question 9 years ago.
At the end of the day, I think the creators give every episode a title because generally every piece of creative work has a title. The audience does need to know the title, but they exist. And since the internet came around, now it’s easy to find what they are.
I think the OP doesn’t go far enough. All shows should also be required to have captions identifying all of the characters who appear on screen and the actors portraying them in order to ease post-show discussions of the episode. For too long we’ve been forced to say things like “the bald-headed bad guy” or “the blonde woman in the red dress”.
I think the shows should also display the actors’ list of past credits so we can be reminded of what that other thing was that we saw them on. But I’m willing to leave that as optional to the discretion of the individual producers.
Also on most of the Treehouse of Horror episodes.
Which most viewers called “the Halloween specials” until about twelve years ago, because they didn’t know the official titles. (See post #35.)
ETA: and the individual THOH segments have had onscreen titles from the start.
If at least two other people on the planet also like the show, then there’s probably a website devoted to it which gives episode titles and synopses.
Cryptic episode titles are nothing new. Most of the old Dragnet radio episodes were called “The Big _____”, where the item named would usually be a minor yet pivotal plot point or piece of evidence. But you usually can’t tell what the story is about from just the episode title.
I guarantee you that if you said to someone — even a huge L&O fan — “I saw ‘Aftershock’ again last night. It was amazing!” they would have no idea what episode you were talking about. But if you said, “I saw the one where they killed Clair Kincaid again last night,” the connection would be made instantly.
Similarly, good luck getting anybody to figure out which episode you’re talking about if you cite “Jeopardy” or “Baby, It’s You” or “Dissonance.”
Oh, yeah, “Jeopardy!” Remember when Ken Jennings said, “What is a hoe?” 
Batman and Superman had them, though perhaps they were titled later, as sometimes happens. For instance, I’m pretty sure the Brady Bunch episode title “Alice Doesn’t Live Here Anymore” was borrowed from the film, despite the BB ep’s having aired earlier.
I just describe episodes by something that happens in the episode. It’s easier to remember that way. Like the episode of WKRP where Mr Carlson is confused about what’s going on at the station or the episode of TBBT where Leonard said something snarky about Sheldon’s behavior. Everyone knows which episode I’m talking about.
nm
“‘Gomer upsets Sergeant Carter’…oh, I’ll never forget that episode!”
I said “Jeopardy,” not Jeopardy!.
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Also, did you see the one a couple of weeks ago when the woman said, “What is dick?”?
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Sesame Street had a four-digit number at the beginning of each episode, probably a serial number of the episode. (Don’t know if they still do that, or why they did. My dad thought maybe it was for teachers who wanted to show it to a class or something.)