Given how hot is it where you live, I trust you can open that coop up A LOT so you don't have baked chicken.
And yes, if you have the skills (minimal for a basic coop) and tools, a build your own will be a lot cheaper, a proper size and being custom, be exactly what you need rather than what someone thinks will work for everyone.
And regarding slope, indoor plumbing drains are spec'ed at 1/4" per foot slope. You don't need much to get water to run off the roof ASSUMING there is no sag, even 1/8"/foot is fine for that. The higher pitched roofs are usually made for volume inside or snow. Even a foot of snow won't slide off a 10/12 pitch roof as long as the temps stay cold. The narrower the apex of the "triangle" the more it can hold (for a given dimensional rafter) because the rafters are running the load more vertically to the top plate which is supported by the vertical walls.
I built this coop with a drill, jigsaw, sander and stapler. I didn't have the money to buy other tools so just used what i can afford at the time. 1st time is a bit more expensive since you have to buy the tools
You will not see it but i left a 3 in gap on the top (all 3 sides) of the coop + ventilation holes. I'm in Arizona so i don't see the point of closing up the coop so i left it open 24/7.. The run is secured. The chickens can come in and out of the coop whenever they want.
It's easy for me. I'll let them out around 6:30PM each day to clean out the run and coop as they free roaming around the yard. They will go back in themselves when i'm done with cleaning + refilling the feeders.
It's easier for me that way since i don't have to wake up at 5-6AM to let them out each day.