I think each scenario you listed is a different answer. We all agree for film/tv shorter is better. If you want a "radio friendly" song shorter is better. But if you want something like Carousel I think a long intro is fine. Carousel is an album opener and wasn't written for radio. Back when people bought albums opening tracks were meant to introduce you to the sound and feel of the album. Another example you would probably understand is Anthem Part 2 from Take Off Your Pants and Jacket. It's got a 45 second intro. I remember buying that album the day it came out, putting it in my car CD player and thinking, "OMG this album is going to be amazing!" All it took for that reassurance was that first 1234!, quiet guitar, 1234!... and when the full drum beat and bass came in...Whether its for film, TV, or just a song being recorded. How long is too long before I have to "trim the fat" in other words.
14 years ago and I still remember the exact moment I first heard that album. That's what music is about.
Michael