A lot of us use mesh as a flooring. I use it in my brooder and in my grow-out coop, both of which are elevated. You'll likely get a lot of people on here panicking about how you are damaging their feet and all that by keeping them on wire, but I've never had that problem.
I use 1/2" hardware cloth. With the chicks, the poop is small enough and they walk on it and scratch it enough that the poop falls on through. When they get older, maybe somewhere around 3 months, the poop is big enough and has a consistency that it will not fall on through. It will build up on the mesh, even with then walking on it and scratching it. I have not tried 1" hardware cloth, but think you might have the same problem. You'd probably still need to rake it off.
One person on here reported that he tried that and rats chewed off the toes of some of his chicks in his brooder. I have not had that problem. I don't know how common that is. Probably pretty rare. Remember that just because something can happen does not mean that it absolutely will happen each and every time. But it is one of those things that if it happens it's 100% and if it doesn't happen it's 0%. And that was in a brooder with them sleeping on the floor. Yours should be sleeping on roosts.
As long as the run is dry I would not worry about them dustbathing in the dried droppings. They will probably keep it scratched out so it is not a huge problem. But you can always try it and see. You can also put a droppings board under the roost to catch a lot of the poop before it hits the ground.
