Whats the point of a sharp key signature, when there are no sharp notes?

im a very experienced musician, i play clarinet alto saxophone and piano. but im just very curious about this. i was playing a sax piece a little while i ago, its just one little practice line, and it had a 1 "#" in the key signature, which would mean to play only one sharp, in my case an F. but there were no Fs in the piece, so all the notes were naturual. so what was the point of having the key signature a sharp?