If you have a truly predator proof coop or predators are not a problem, then there is no strong reason to have a door on the coop. Possibly temperature control, drafts, or rain blowing in could be potential problems to consider. I do find it very difficult to build a truly predator-proof run unless you are building one of those very small runs totally enclosed in hardware cloth, which is a possibility in the city.
Before you assume you have no predators in your city, I suggest you call your animal control and chat with them about raccoons, possums, foxes, coyotes and skunks. Feral cats are usually not a problem with full grown chickens, but your neighbor's dog could be.
I find the inconvenience of opening the door in the morning and closing it up at night is well worth the extra security, but some people are content to not do that. My parents lived in the country and never closed the coop door. They had no run, just let the chickens free range. Sometimes they would go years in between predator attacks, but then they would have a fox or dog to deal with.
good luck!