There's probably an interesting (to us nerds, anyway!) story to be told about the history of not just reels but all consumer pre-recorded tapes. In my library I have several allegedly made by obscure companies that you never hear about any more. As far as I can tell, the only labels that made their own reels were RCA and Columbia while everyone else farmed out to Bell & Howell, Ampex, Bel Canto, Stereotape, Magtec, etc. And I assume some of those now-obscure ones became or merged with the bigger (relatively speaking) names.
RCA clearly stopped making their own reels by the 1970s but Columbia continued until 1980 or so, if for no other reason than to offer that format for releases they figured would sell enough copies through the record club.
Columbia was also apparently making at least a few retail reels for other labels. A&M comes to mind...I've got two Joe Cocker reels that, based on the boxes (horizontal opening, full color on both sides) and gray spools appear to be Columbia's work. Unlike Ampex and Stereotape, there's no explicit manufacturer listed, but Columbia had a style and those follow it.
It's not at all clear to me what the story was with cassettes and 8-tracks. I know Ampex made some of them for the labels early on (and Ampex even re-released some older albums on cassette using "Ampex" as the actual label!), but I don't know if or how often that stuff was brought in-house once the formats were clearly established as winners.
But then it gets even murkier when you realize that not all the major labels pressed their own vinyl. There's a lot of other-label stuff that was clearly pressed by Columbia or RCA, just for two examples. When you look at Discogs you realize that once upon a time there were TONS of independent pressing plants not tied to any label at all. I'm pretty sure Warner Bros. didn't have their own pressing plant until not long before CD came along.
Anyway, if someone wants to write a book about this, I promise to buy it!