If you never plan on closing the coop door then don't waste the time and money building one. It's only function is predator protection at night and weather shielding. Well, a roof keeps out rain and snow and a few walls stop the wind. Put the money saved for no coop and purchase bulk hardware cloth. Your significant other is right in that chickens are not stupid and can get away from most predators. Problem is if they are confined then you've taken away their main survival techniques- ducking for cover, running away and flying to tree limbs. If in a shoddy run they are merely corralled to make it easier for a predator that gets in to take all of them.
Using a coop is far cheaper than making a run 100% predator proof. It's easy to keep day predators out of the run. Welded wire like the common and inexpensive 2x4" 14 gauge fencing can't be chewed through or pushed through by dogs. Make an apron of same welded wire 18-24 inches out from run laying flat. Put under sod or stake down allowing grass to grow through then you can mow it. Welded wire comes in 4 foot by 50 foot rolls commonly for under $40. Lengths of that cut in half gives your the dig proof apron. That is a daytime predator proof run. Weasels can easily get in. That's what the coop is for and cheaper to put 1/2 inch hardware cloth (pricey stuff) on coop openings and lock the door at night, every night.
Another option that I use spring summer and fall is electric poultry netting. Makes for a huge movable run that will stop all land predators, excepting weasel. Put fencing around a few bushes and or trees so the birds can duck for cover when large birds are in the sky. Lock the coop every night.
Then there is always automatic coop doors for those that can't get up in morning to let birds out or don't have neighbors that will tend to birds when on vacation. Opens and closes via light sensor, runs off battery.