We also fought a lot when it came to the early days of torrenting anime and movies. I don't think Streaming and QuickTime really ever cross paths. It just didn't support as many fancy features that VLC and Media Player with the various Codec packs did, and later on players like MPV absolutely overwhelmed QuickTime in terms of playback and feature sets.
I have vague memories that QuickTime used to come with the iTunes package for Windows, but I may be wrong on this so don't quote me on it. I do distinctly remember a period of time when many people who had Windows would ask how QuickTime got on their system.
From the Mac side of things, QuickTime always felt like it didn't know what it should be. It was aways a sort-of media player without all the library features and playback features the other players had, along with a very basic media editor, media converter/exporter, and a few other bells and whistles that were neat but no one used and very few people wanted to pay for.
Eventually I think Apple just realized there was no sense in maintaining it as a priority. As I wrote this post, I realized that on Big Sur, the dictionary no longer corrects QuickTime like it corrects iTunes or iMac or many other Apple products. (amusingly, apple seems to have had the self restraint not to assume you mean the company and not the fruit when writing apple, just a neat little fact ;))
Ultimately though, I don't think streaming and QuickTime really were enemies at all. I don't think streaming was even really a thing by the time QuickTime was really relegated to "that app you accidentally open movies in sometimes." Now it just is a media player that sticks around because you have to have a media player with your OS or the other OSes will make fun of you.