I won't get in the middle of an argument between Husband and Wife! But I can tell you what my experience has been, and what has/has not worked, and what I plan to do in the future. My 5 girls have a winter time run that is 20' x 30' as well as a predator proof run/sunroom that is 8 x 8 with an additional 4 x 8 that is partially predator proof (the 8 x 8 is covered with 1/2" hdw. cloth, and the 4 x 8 is covered with 1" chicken wire, both covered with 4 mil. plastic to make a warm sun room) In the summer, they have a 1600 s.f. run that is moveable and enclosed with electric poultry netting. They are allowed out to free range in the warmer months when I am home, and can keep an eye out for dogs/hawks, and any other dangers. Last summer, I had to herd them out of the garden until it got grown enough that they couldn't destroy it. It was a constant chore to keep them away from the blueberries and greens. This summer, I plan to close in the garden with deer fencing to keep them out. I am also changing the lay out of my garden into more 4' wide beds with 4' paths, and will put up fencing here and there to close in a bed, or allow them access to the space between beds. I also have a 3' x 6' tractor, and may make a second one to allow them to range safely over a bed or between beds without destroying the whole garden.
So... in answer to your questions: It is not essential to free range chickens. Lots of people keep them just fine in a coop and an enclosed run. If you keep them in a run, they WILL destroy all of the vegetation. Last summer, if I hadn't moved my 1600 s.f. run, they would have removed at least 75% of the vegetation, and would certainly complete the job this spring! In a smaller run, I'd recommend doing a deep litter in the run itself to prevent excessive nutrient build up in the soil, and run off. It will also prevent the run from turning into a fly infested mud pit/dust bowl/moon scape. (depending on your weather.) And it will give the girls something to do. They love to forage in deep litter for bugs and what ever else they find to eat.
Now, your wife is approaching the idea of having chickens from a completely different paradigm. Of course she is... If you both agreed on every thing, one of you would not be necessary! She envisions chickens as being mobile lawn ornaments, with a side benefit of providing free fertilizer, weed control, lawn clipping, and bug control. This is the reason I got chickens, with the eggs being a mere bonus. Your lawn ornaments will leave fertilizer bombs indiscriminately where ever they go. If they want to go on your deck, they will. (though mine have yet to be bold enough to venture up onto the deck or even up my front steps) They will dust bathe in your flower beds, they will destroy your newly planted garden seedlings, They will definitely scratch all of the mulch out of your flower beds... and they will do it all with great enthusiasm and chortle with glee while doing it. If they are allowed to free range, you'll have to provide the fencing to keep them where you want/or don't want them, supervise to keep them out of trouble. There is also the increased risk of predators, as every body likes chicken.
Have fun deciding what to do, and realize that it doesn't have to be an all or none decision. They will need a run for safety, b/c if they don't, they won't survive long in this chicken loving world, but you can let them out for supervised free range as time and mood allows!