I use 2x4 welded wire for my run.
But I also have a large dog in the backyard. Any predator in the backyard gets promptly run up a tree or back over the privacy fence.
Best predator defense is a chicken friendly dog.
I say yes. Sooner or later you will need to lock them up for one reason or another.
I dont lock my coop door every night but there have been times when I needed too.