Hi, welcome to the forum, glad you joined.
What breeds of chickens? Some have more trouble flying than others. That might factor in.
Most chickens like to sleep on the highest point available. And most can fly much better than many people imagine. My full sized fowl have no problems flying up or down from my 5' high roosts. When I was a kid on the farm some of our full sized fowl hens would fly up to a 10' high hay loft to try to hide a nest from us. They'd fly back down. It was my chore to find those nests. As a kid on the farm I saw hens roost in trees higher than 7-1/2 feet. I've read a few posts on here of chickens roosting more than15 feet up on something. It's often bantams when they are that high.
The higher the roost the more clear space you generally want them to have to fly down. With a 16' x 12' that should not be a problem. I've had chickens, mostly hens but also a mature rooster, launch from my 5' high roosts, fly about 8 feet forward, hang a sharp left, fly out of the coop human door, and land in the run. As long as they have some room they do OK.
A good way to inspect or treat your chickens is to take them off the roost at night when it is dark and using a small light. There can be a benefit to having the roosts low enough to pick them off at night.
I don't know what that shed looks like, what intermediate launch points they may have to help them fly up there, anything like that. In my opinion. if they can get themselves up there I'd be OK with it. Others will have different opinions.