Though, you mention soaps.

Yep. Soaps were the main exception - entirely serialized, with story lines running for years, of not decades (as you mentioned). There just wasn't any expectation that those stories would be good or sophisticated, for basically the same reason. You had daytime soaps that were targeting a specific audience at a time of day (housewives or the elderly) when they probably would always be available to tune in - and the plotlines progressed at a slow enough (and predictable enough) pace that if you missed a day you wouldn't be lost. And even then, you had a solid amount of print media (Soap Opera Digest) to help you catch up on the plot points if you needed it. And then the nighttime soaps just carried that formula.

But for the most part, it wasn't until Hill Street Blues that there was a serious effort to tell a sophisticated story that crossed multiple episodes, where if you didn't watch an earlier episode in sequence you would be missing out on some nuance or subtle point that made later episodes more interesting.

I pointed to technology, but it's more generally a story about the distribution of television as affected by that technology. Up until about 1980, television had to be watched when it was on, and there were only a handful of channels. Almost every show (soaps excepted) had to consist of largely stand-alone episodes that could be (mostly) fully intelligible to people who had missed prior episodes, and had to appeal to as large an audience as possible. And if you wanted to join a show in progress, there was literally no way to watch episodes from previous seasons except the serendipity of re-runs.

In the early 1980's, you had the rise of three major technologies that changed TV distribution: the remote control became standard on many TV's, VCR's started being adopted, and cable television reached significant penetration. The remote control and cable TV broke the network oligopoly and allowed for economically viable smaller channels, launching the multi-channel transition in TV. Shows no longer needed to (potentially) appeal to nearly everyone to make economic sense. And as mentioned upthread, the VCR allowed people to make shows that depended on having seen prior episodes in order, rather than self-contained units.

That's when you start to see the earliest experiments in actual serialized storytelling, because now the distribution allowed for it. Hill Street had story arcs that ran for entire seasons, and as VCR's (and later DVR's) expanded, you saw more and more of that in the 1990's (Twin Peaks, X-files, NYPD Blue, Babylon V, Buffy, and others).

By the late 1990's/early 2000's, when DVR's and DVD's started coming out, everything was in place. You could create a television show where every major storyline could play out over as many episodes as you wanted it to, and people had enough of a safety net that they could decide to watch every episode without having to commit to being at home during the airdate. You also had a distribution channel with box sets in video stores where people could catch up and watch an entire series' prior seasons. For the first time, you could make television where a new season of the show (say, season 3 of a series) could tell stories that depended on viewers having a deep understanding of the characters and their histories from earlier seasons - which made for a much richer television experience.

And thus came forward The Sopranos, and Peak TV was born.