Every so often, you need to do bigger chores, like go buy fees or fix something in your setup. A couple times a year you need to do a deep clean of the coop (throw out all the straw, scrape any poo that's collected on the floor or wherever, put in clean straw). Sometimes a chicken dies, and that's not fun, but it is something you have dispose of properly.
Ultimately, though, it's a hobby. It should be fun or relaxing most of the time or else it's not worth it. Like gardening or running a home server. If you're trying to just save money, maybe you can save a tiny bit in this particular moment, but there are surely better ways to save a few bucks.
I ask because I used to have a good sized garden at my old house, growing enough veggies to both preserve and distribute to neighbors because I grossly underestimated the yield. While it was nice to have the neighbors love me, it was also a lot more work than I had bargained for (especially when otherwise working 40+ hours per week) and it got me thinking about community gardens and whatnot, why those might make more sense these days
I'd still say that if the primary goal is saving money, there are better options to consider. If there are 20 single family homes living the "default" lifestyle of such a home, there are probably more than 20 cars (probably approaching 40). Can this community work out a system of sharing cars (and the costs associated with those cars)? How few cars can this group of people reasonably get by with if they are sharing?
Another option is having one big tool shed where everything inside is shared. Each single family home, by default, would probably own their own lawn mower. But a community of 20 households probably only needs to own one or two.
That said, I think there are other benefits of a big community project like a community chicken coop. It's good for building relationships with other people, it's fun, and the eggs do taste good. You could draw up a simple calendar and decide who is responsible for taking care of the chickens each day if you wanted, and that'd probably make things easy (although, tbh, one or two people will probably need to be "in charge" of the chicken coop, and following up if something falls through the cracks). A community chicken coop also makes it much easier to take a week-long vacation or whatever, because you know that someone will take care of things. When we had a chicken coop (in our single family house, not part of a larger community), finding someone to care for it was kind of a large task before we could actually leave our home for an extended amount of time.