We've had
chickens before, and I'm going to get
chickens again in a couple of years, so my take on it is as follows:
It's not a lack of depth perception that's the problem, it's
chicken's survival/navigation mode.
Chickens are dinosaurs that evolved to live in forests. They like to roost high because it gets them away from the ground where the night-time predators prowl. Perches equate to branches in a tree. Climbing to higher and higher perches is the same as climbing to higher and higher branches. Not being able to see out is mentally equated to not being able to
be seen. The problem with that is that as you go higher in a tree, the number of small twigs tends to increase, making the "flapping of wings" a tricky proposition. A chicken that can't flap it's wings in clear space will fall like a brick if it slips on the way down. That's why they don't like climbing down — limited flap room results in an increased chance of injury... and an injured bird is a dead bird.
I noticed years ago with our chickens that in the morning they would happily 'aim for' something that looks like a 'break in the foliage' (aka, an exit — brighter on the outside than on the inside). We had a big coop with perches rising up from one side like bleachers to the middle, and the other half being open for humans to access, and the external wall of that bottom area being open to the run. The chickens would climb up to the top perch, stay there all night, then simply fly/flutter down the open half towards the well-lit exit on the opposite wall. None ever got injured as far as I'm aware. The top perch was about 1.8m off the ground.
Most coop designs I see have the perches get higher and higher towards a back wall. This makes sense for humans, but not for chickens, as it doesn't 'work like a tree'. If you design your coop and perches so the chickens can 'hop their way up' to the tallest perch, then 'fly/flutter down' towards a well-lit and obvious exit in the morning — through an open space clear of obstructions — then I think the chickens will do fine.