I recall a couple occasions:
- Didn't want to open a browser one day but wanted to download the latest version of FF. Thought I'd try FTP. Ultimately gave up on trying to find the right path and Googled it.
Another time (later), I vaguely recall being at a kiosk with IE disabled in various boring ways, and I tried to see if I could download FF (just to see if it was possible) after successfully managing to open the FTP site. I might be misremembering, but I think the only reason I was able to locate the dir properly was because I'd previously made a careful mental note where it was. (It downloaded, but executables were disabled. Those sysadmins did a good job.)
True story: Back when I was doing desktop tech support, downloading Ad Aware via command line FTP was a favored method of mine when the user's browser was so fucked by spyware that it was inoperative.
I'm not aware of any popular OS that doesn't have ftp support on the main UI (except Android, which doesn't have a file management app anyways; not sure about iOS). Nautilus has ftp support. So does thunar, dolphin, konq, etc. You can type ftp addresses into the address bar in osx, iirc.