At the time I used it (around 2006), I don't believe QuickTime was required, but it was Trojan-horsed onto me every time iTunes updated. It was an opt-out, and Apple definitely fostered the impression that it was required (it was for some features I guess).
It also hijacked file associations without warning, which was one of the most annoying/aggressive things about it.
I'll also add that having to install bloated garbage like iTunes in the first place was aggressive (due to Apple's policy of locking iPod owners into using iTunes), so adding another piece of bloated garbage on top of that was really irritating.
When I was dealing with it, it wasn't required and it was pushed - installed by default with iTunes IIRC, which of course meant that this unnecessary software was installed for almost all users.
It's not common, but the product my work makes uses it as a cross-browser, cross-platform (Windows and OS X) way of embedding video into a web page with good scrubbing and multitrack audio support.
We're replacing it with native HTML video, but comparing the number of workarounds and shims needed to get feature parity across browsers and platforms, Quicktime is certainly the easier choice. It's just not future proof.
If you’re using a relatively recent version of OS X, Quicktime Player is mostly just a first-party front end for the Quicktime-replacing AV frameworks that got ported to OS X from iOS a few versions back. It probably keeps the Quicktime name only for legacy reasons and so upgraders aren’t confused as to where the default media player disappeared to.
