We have a combination enclosed coop/run and we put hardware cloth around the entire thing including the roof. The reason we did this is twofold: A) our Spanish-speaking-only neighbors across the alley have a young dog that they let roam wherever (he's going to get hit by a car driving along the alley, eventually, but . . . ) and the dog is known for chasing wild birds like crows and robins, and B) we also have a semi-wild alley cat, who I personally have seen stalking crows.
I don't doubt for a second that those two animals will consider our new pullets a lunch buffet, so we're taking precautions. There will be a real roof (which we're creating this week) on our run in addition to the hardware cloth, we're padlocking all three doors, the nest boxes are *inside* the raised hen house, we're going to put down an apron as well, and on two sides of the coop/run (basically, the far corner, where a predator would most likely come from), it's also protected by a 4' chain link fence.
We hope that predators (including humans!) will discover that there are easier alternatives and leave our birds alone.
We put hardware cloth on the top because we have smart squirrels. And when we were framing our enclosure, wild birds loved it and would perch as though they owned it! We need to keep them out too -- we don't want to feed the entire sparrow population of Central Minnesota with our chicken feed!
We do know that the hardware cloth, even without tying the ends together (ours was only 12" deep!) is strong enough as it is right now to keep a charging 40ish pound dog out . . . one of our Standard Poodles got crazy when she saw the Spanish neighbor's dog in the alley and forgot the coop was there (this was a scant 24 hours after we'd put the cloth on!) and she barreled right smack dab into the side of the coop and therefore quite literally bounced off the cloth. The cloth still looks newly installed.
She shook herself a couple times and pranced right off, defending her yard -- and has now been quite careful since to avoid getting anywhere near the coop, LOL. If the hardware cloth is strong enough to easily rebuff a 24" high (at the shoulder) 40# dog in full flight, it ought to stand up to just about anything.
Nevertheless, we also know that a determined predator is a different thing than a goofy dog forgetting where large objects in the yard are.
I say, put hardware cloth everywhere . . . you never know where it might keep a predator out and save your birds.
Whitewater