Cliff-hangers long predate modern television, and seem to be endemic to any serialized content. The term itself dates back to the late 1800s, and it’s use has been derided in every medium from books to radio to film to television.
It also wasn’t a purely American thing. Go watch some of the old black-and-white Dr. Who episodes, for example; you’ll see some prime examples of cliffhanger- and recap-dominated television.
The exception seems to be late-20th-century television shows, where the syndication system meant that episodes might be dropped or reordered arbitrarily by the local station. This made it difficult to impossible to have any kind of changing circumstances like an overarching plot except at big events like season breaks. Star Trek: TNG is a good example here; the interpersonal relationships between characters don’t really evolve very much, and when they do it’s part of a season-break spanning two-part story. Those reliably had every character in danger at the break to provide the studio leverage during contract negotiations.
As the premium television channels started getting into producing their own shows, they didn’t have the problem of local affiliates reshuffling their schedule— their distribution model let shows have an overall plot, but they still add to be acceptable for viewers that expected to get a whole story each week. This gave us shows like Stargate SG-1 which still had very formulaic episodes, but also a continuity between them.
You also started to have the national networks assert more control over the local stations which led to some successful attempts at shows with both series- and episode-long plot structures, like Babylon 5 & the West Wing. Vestiges of the old system remained for quite a while, though, and is a large part of why Firefly was never commercially successful— it was produced with continuity from episode to episode in mind, but the network aired them in a seemingly random order instead.
https://en.m.wikipedia.org/wiki/Cliffhanger