In this piece by Clark Throssell, Ph.D., Tom Voigt. Ph.D., turfgrass scientist at the University of Illinois, discusses the possibility of using an unmown, cool-season grass as a playable rough. And, at least for the midwest, it really isn't possible. Conditions in the region are ideal for cool-season grasses, and so dense stands form throughout the season, making shots difficult for even experienced golfers. However, in areas like Ireland, Scotland and England, unmown playable rough is possible (with a careful balance of water and nutrients).
Fine fescue was also tested in the midwest region and found to be still too dense for unmown playability.
Check out this article for more information on different grass types in both playable and unplayable rough areas, or click the link below.