Steve,
Mr. Decker makes a good point about the green collar relative to maintenance, but I also think the green collar developed as a response to balls rolling up against 2-inches (or more) of grass immediately adjacent to the green - as a buffer between the putting surface and the rough, if that makes sense.
I could be wrong, but if memory serves correctly I think Baltimore Country Club eliminated the collar cut in recent years (might have been another vintage course, but I want to say Baltimore for some reason). Anyone, correct me if I'm wrong. Wherever it was, I wonder how it worked out? Relative to playability around the greens, I bet there was a lot of complaining!
Where I consult, I recommend reducing the collar cut to a width the golf course superintendent is comfortable dealing with (as narrow as possible, that is). This gets the actual putting surface as close as possible to surrounding slopes and hazards... and, it just looks better in my opinion. Especially at vintage courses.