The main reason has little to do with any of that, but just historical inertia.
There's a lot of species that could have potentially replaced the chicken if we unwind human history and started anew, but it's not a competition between wild species of birds today, but chickens with at least 5000 years of human-guided domestication v.s. most other species.
The same can be said about pretty much anything people eat and farm. Most modern fruit and vegetables were pretty much inedible in their primordial pre-domesticated forms, it's only through thousands of years of effort that we have what we've got today.
In terms innate qualities making chickens suitable for domestication over other birds, some of those are probably:
1. They're pretty much flightless[1], even in the wild. This excludes most bird species right off the bat. Hard to domesticate something that'll just fly away.
2. They're comfortable in groups, and have a group hierarchy. This tends to be common among species humans have domesticated. Good luck domesticating e.g. birds of pray productively, they'll constantly be fighting each other for territory.
3. They're not picky about food, and don't require humans to actively feed them in the context of pre-industrial village life. Some birds only eat say insects, chickens can eat pretty much anything, even other chicken.
Separately, I’m more interested in why chickens are more economically efficient than, say, pigs or cows than why they’re more efficient than other birds. Any thoughts there?
1. Small animal which requires less bone structure to support (bone scales non-linearly with mass for land animals).
2. Shorter lifespan and use of eggs allows simpler and quicker sexual selection.
3. Less intelligent animal so less energy and nutrition spent on growing the brain and maintaining its function.
Its a smaller animal, basically. Fish and insects are more efficient than chickens.
https://ib.bioninja.com.au/_Media/feed-conversion_med.jpeg