What is a Monitor roof? A roof with shingles? Or specific wooden bracing inside?Things we did right:
I would heartily recommend a monitor roof for anyone in a hot climate. With the pop door open 24/7 except in dire emergencies and the coop located in deep shade it was never any warmer inside than the ambient air temperature outside and, as previously noted, no rain ever penetrated beyond the roof overhangs.
Nor was it hard to build for a competent handyman.
The structure is entirely sound, due to DH's family habit of over-engineering everything -- though it can be moved by 4 men with the carrying 2x4's in place (we knew we'd be moving to the country eventually). The skids need to be replaced, but that can be accomplished by putting it on blocks during the process.
It *is* portable, though not so light as to be moved without serious effort.
The nest boxes were a good size even for the Brahmas.
The roost was well-placed, above the nest boxes but below the open section of the roof.
The hardware cloth defeated the efforts of a predator -- unable to tear the wire loose it attempted to rip through and failed (we added a second layer over the entire area that was damaged).
It was not difficult to clean out since the large door allowed me to reach all portions of the coop with the manure fork even though I am too short to quite reach the far wall. When the residents retired the man helping me relocate them to the freezer was easily able to reach in and get hold of them without a rodeo. (I would not make a non-walk-in coop any deeper).
The far half of the run was roofed, so that I could keep the food and water out of the coop. The chickens were able to bask in the morning sun and had to get out of the coop for exercise in all weathers. (In a sunnier location the entire run should be roofed.
We had a perch in the run, which was regularly used.