My coop and run are fully enclosed with 1/4 in hardware cloth. My coop doesn't have a door to close it off from the run, do I need one? The top and sides of the run are fully sealed with hardware cloth.
My coop is linked in my signature. It's a cattle pane; hoop coop covered in hardware cloth. It has an interior coop, but that coop has no roof, or door - it's essentially a windbreak for them to huddle up in the winter time and an area to increase the square footage of my coop. They have access to the entire 8.8' x 16' coop at all times (the raised coop w/o door and roof adds another 8.8' x 8'. If your run is secure, there is no need to lock them up in a smaller box within a secure run.
You're the only one who knows how secure your run is. I have a door between my coop and run, but never shut it at night. (That's gonna come back and bite me some day, I know). I have 2x4" welded wire for the sides and top of my coop. It keeps the big predators out, but will hardly be a speed bump for a mink or weasel.
Lately I haven't been shutting the doors at night but I still think that it's important to have one in case you do ever need to shut it. If you go on vacation or something they can be locked in or left open until they get there. Or if you want to clean the coop or the run you can lock them in or out of one or the other to prevent escapees. This is especially important if you're like me and your cleanout door is outside of the run. If I don't lock them out they'll get into the yard! Anyway, I say you need a door. You may not ever need it but if you do you won't scramble to build one