> What fair use argument can be made for just having GameOfThrones.mp4 on my web server for people to download?

The server operator isn't the one using it.

Is it possible for anyone to make any fair use of GameOfThrones.mp4? Presumably yes, under some set of circumstances. And then the server operator has put it there for the people who want to use it in that way.

Some people might then use it in some other way, but some people might borrow a book from the library and then use it to author an infringing derivative work. Why should that be the responsibility of the library rather than the party using it in an infringing way?