You are going to get some different opinions because there is no one right answer for everyone. There is a rule of thumb many use that says you need 4 square feet per chicken in the coop along with 10 square feet per chicken in the run. This rule of thumb is intended to keep practically all of us out of trouble regardless of our chickens our climate and our management techniques. It is more than many of us need, but there are some people with certain climates or management techniques that actually need more. We are all different with different situations.
One kind of trouble I am talking about is behavioral problems. If chickens are too crowded, they can become bored. When I say "can" I do not mean it will absolutely happen each and every time without a shadow of a doubt without possibility of exceptions. It means it might happen. They might become feather-pickers or even go as far as becoming cannibals. Social unrest is possible. There are different degrees and outlets for behavioral problems. Even in fairly crowded conditions, some will be fine. That's why I hate giving hard and fast numbers. There are always exceptions. And space includes coop, run, and free range as a system. You can't talk just about the coop and ignore he rest. If they can get out of the coop to more space, then your coop can be smaller.
Another issue with crowding them is you might have to work harder. A prime example is poop management. I'm a firm believer that the fewer times you have to clean out the coop, the better. But I have an 8' x 12' walk-in coop, not a small elevated coop where all you have to do is pull up a wheelbarrow and sweep it out. The more space they have, the more poop load it can carry, but you still might have to give special attention to under the roost. They do poop a lot when they roost.
Another more nebulous concern I have is that if you limit your space, you have less flexibility in managing them. On the good days, what you have will probably work well for six chickens, especially if you can let them out to roam a little daily and don't leave them locked in the coop very much during their waking hours. But what happens if you get a freak storm where they cannot get out, even to the run? Or you get a predator where you don't feel comfortable letting them out? You may be able to avoid some of these problems by making sure the run is usable year around, but that may involve a commitment to keep snow and wind out of it. Mine don't mind the cold temperatures, but they hate a cold wind. Mine don't like snow when they first see it, but if it stays in the ground a few days, some get brave enough to walk in it. You may need to scatter straw or something on top of the snow to get them into the run. This involves a commitment to do it when needed and you may have to clean it up when the snow thaws.
What you are proposing would probably work, but you may find you need to work a bit harder than I do and you may have to tweak the normal management techniques a bit, especially during bad weather. People do it, but I'll admit to being a tad lazy sometimes.