Regarding of anyone actually did Waterfall. I worked in a company back in the early 80s that was small and 5 of us worked together in an Agile-like manner with a marketing lead as our “customer” along with a tech writer and a test lead.

As I began to work for larger organizations after that, a phased sequential approach was the model being used. So it seems to me that larger organizations, as an organizational model, did follow a waterfall-like approach where all effort in a given phase (requirements, then (arch) design, then coding, then integration testing, then system testing) would (attempt to) be completed before moving on to the next. I say “attempt to” since there was always backtracking of some sort as people learned things. But the official model was definitely waterfall.

Clearly, people worked in a lot of different ways in smaller organizations, but waterfall in large organizations help support a soloed company structure (or vice versa). So waterfall was, and is, there for large companies and government organizations even as they try to implement a more Agile framework.