Welcome to BYC.
The Usual Guidelines
For each adult, standard-sized hen you need:
- 4 square feet in the coop (.37 square meters)
- 10 square feet in the run (.93 square meters),
- 1 linear foot of roost (.3 meters),
- 1/4 of a nest box,
- And 1 square foot (.09 square meters) of permanent, 24/7/365 ventilation, preferably located over the birds' heads when they're sitting on the roost.
These are not hard-and-fast
rules, and here is
an article explaining why, but they are suggested
minimums.
How many chickens do you have and what is the square footage of the coop in question?
Omelet coops are generally considered better built than most prefabs, but they are notoriously short of ventilation and, like almost all prefabs, wildly exaggerate the number of hens they can hold -- basing number claims on legal requirements for commercially-kept, intensively-managed birds rather than best practices in backyard conditions.
As to your final thought, this is from an article that I'm writing:
But I free range/have a huge run and my chickens only use the coop to sleep and lay eggs! Why do I need all that space inside?
You might not. As I've said, these are guidelines, not hard-and-fast rules.
If you never close the pop door so that your coop and run function together as a fully integrated system that is the equivalent of a huge, open-air coop, then your flock might be just fine for years, even decades.
If you are always out there to open the pop door at the crack of dawn or you have an ultra-reliable automatic door so that your chickens never lack access to their free range territory during the daylight hours, then your flock might be just fine for years, even decades
If you live in a mild climate where chickens can always go out into their run/range and are never kept in by snow or storms, then your flock might be just fine for decades. People who keep chickens in places with tropical and subtropical climates do successfully go without a coop at all, just offering a covered roost and some nestboxes.
But when something happens ...
When a determined predator moves in and breaks through the fencing so that you have to confine the flock to the coop itself so that you can fix the run,
When an extreme weather event prevents your chickens from leaving shelter for days,
When an emergency calls you out of town and you can't find someone willing to be there at the crack of dawn to open the pop door,
Then you could have a mess on your hands.
Which brings us back to the issue of flexibility and options. Any time you push a system hard against it's limits you have to count on everything remaining stable -- exactly as it is without any changes. How well that's likely to work depends on your specific circumstances. You may never encounter an unfortunate circumstance -- some people DO hit the lottery, after all.

The current something that has happened for many of us is Avian Flu -- which means that our chickens are not free to roam in their large pens or to free range on large property but are confined to areas with roofs and wire so that they have no contact with wild birds or their droppings.