Snakes are a risk to chicks and eggs but shouldn't be too much of a problem for larger chickens. If you put a strip of hardware cloth around the entire bottom of the coop (maybe 24" instead of 36" to save some cost) you can protect them from all other predators other than snakes. From your pictures, it looks like you may be rural/suburban enough to have snakes.
My two-cents is that you have to decide what level of risk you want to allow. People raised chickens without fences for a long time, or just light chicken wire once they did have fences. They also sometimes lost some chickens. Only you can decide what's best for you.