Spoiler Alert: It does.not.save.money. But the eggs are way better and the chickens are happy. Layer hens on egg farms live in a cage the size of a milk crate their whole life.
Can tell by the pictures of the coops that you are correct for 'most' of the people posting here. They are spending BIG money for some 'free' eggs.
Big $$$ on coops, big $$$ on fancy birds, big $$$ on feed most likely. Yeah, the majority are paying ten times more for those 'free' eggs AND they get to clean up the poop!
FWIW - Your honestly (in darn near every post you make) is something that I really appreciate. Have read enough of your posts here now to know that you don't 'candy coat' anything and pretty much just stick to facts and 'telling it like it is'.
I went the opposite route when I did my chickens and yes I DID save a good bit of money on my eggs.
The coop in my case was free thanks to spare building materials from work and my spare time putting it all together. No doubt it 'would' have cost me several hundred dollars 'if' I had to pay someone else for something similar. It is ungodly what places like TSC charge for a tiny little rinky dink coop these days. Most people don't have the skills, tools or the patience to even try to build their own so they are stuck paying those rapey prices for their coops. They are way in the hole as far as the dollars are concerned long before they ever see the first egg.
My birds were the cheapest red pullets that the local TSC had. (didn't care about 'pretty' birds - I wanted egg layers and that was all)
The feed was not nearly as expensive as it could have been either. People pay a lot more for those bags of whatever at the TSC when in a lot of cases they 'could' have asked around and found a local co-op where they could have bought in bulk for a good bit less money. Not to mention free ranging the things in the yard. Chickens will pretty much eat anything. (including your yard)
I used to think that when I peeled an onion, peeled some potatoes or diced up a green pepper that the left over bits were garbage. Hell no, That stuff is tasty chicken treats! No such thing as vegetable matter going to waste!

Have a big rain and notice a lot of worms on the driveway? Ohh yes, my butt was out there with a bucket picking up those worms collecting chicken feed for FREE!

Have a piece of meat that sat around in the fridge too long to where you can't even consider it fit for doggie disposal? THAT same piece of meat can go off in a chub bucket and will produce piles of maggots (chicken treats) for several days. (chub bucket - a bucket with holes drilled in the bottom to allow the maggots to drop out but not the nasty meat hung high in the chicken area)
I never gave away 'free' eggs to anyone. Any and all eggs that did not go in MY tummy were dog food for my girls at the time. (saving me $$$ on kibble)
A chicken of mine past egg producing age was not 'kept around' as a pet either. That joker was destined for the crock pot or dog food. Was never bought or intended to be any sort of 'pet'. No way, no how. They were bought to inexpensively produce FOOD for me and the girls and nothing more.