After thinking a bit more about it "next exit" is the most immediate if you don't see any exits. If you are getting close to an exit you see and ask "is this our exit?" the answer can be "no, not this but next exit", or when giving directions you can say "not this exit, but next".

Language is not easy and full of ambiguity, which is why language majors haven't taken over software development

And you're always "in sight" of a Friday, so "this Friday" could always be in play :)

I suspect it's something to do with how we bundle days together into weeks. "Next Friday" really means the Friday of next week. It's even less certain when we talk about Mondays and Sundays depending on which day you regard as the start of the week.