The Tzedaka part is mentioned as an extra Zchus. It is not part of the original idea.
While the theory of the chicken being used simply because everyone had it is mentioned by the Gaon quoted in the Tur as a viable reason, he goes on to explain that it is purposely used. This is further held up by the Maharal and Arizal. We have been using it long after Bavel. In France, Spain and Germany and in most places, Jews lived in cities and did not have the option of moving to suburbs.
Historical theories are nice but to use them as a Taana on others is pushing it.