Not really sure why you felt that needed further qualification.
Existence is not a relative parameter, something either does or does not exist. There's not much point in saying something doesn't exist except in those cases where it does.
No one is arguing that the key is common or useful in most situations. It's the sort of thing you get to while working on a graduate degree in music or maybe in the pit band in a Sondheim musical and then never need again.
Glad you finally said this last as your posts up to this point may have led someone new to all this to believe otherwise....which is why I "felt the need for further qualification" as you put it. Sure it "exists" but not in any useful way in 99% of the situations most people will ever encounter.
As far as existence being a finite parameter it's not but rather is relative to your conscious experience. Music theory is a construct of the human mind and will cease to exist when you cease thinking about it. It will change as you change how you think about it. But that's probably for another thread.