Why have green collars and first cut of rough?
In addition to the maintenance and aesthetic purposes cited, for definition. To orient the golfer toward the lines of play; as a frame or point of reference to better gauge the point or position of the desired target.
Preston Trail's greens have a unique mowing pattern. The greens are cut to a relatively short height, then there is an intermediate fringe of 18" - 24" just a tad longer, a slightly longer primary fringe of similar width, then the 2' - 4" rough.
Shady Oaks, Hogan's hangout for the last 20 years or so of his life, had only very short rough (1'' or so) around expansive fairways. I have never played a course with just two cuts, one for greens and one for the remainder. It would be pretty interesting.