YY to a roof for them. Cats, foxes, birds of prey, magpies. All foe of the piggies -- though it would have to be flipping strong to carry of GP4
If you could put their hutch inside the run and give them hidey places they'd love it. But you might want a second moveable run because they can denude a patch of grass in a few days . So in their run they can pootle about and have some extra grazing in the moveable one.
You need to plan where you site it - out of full sun. Away from draughts in case your jutch gets blown over. Good drainage. Protect the legs of the hutch against damp. And make sure you can shut them in if you don't want them going out.
I have a big wooden 'box' in the run (it was a chest of drawers that I took the innards out of and DH treated it with petsafe paint)
Rubber trugs upside down with a door cut out
And they love their 'Hop Inn' tunnels.
Chicken coops look good, different areas to sleep and hide but the ramps are steep so you'd need to customise it for lardy pigs. Some are 'walk in' size for humans.
Mine have a playhouse that DH customised for pigs.