Catholic Churches do plenty of community meals - just not around mass. This is likely due to the former requirement to fast proper to communion.
I'm extremely skeptical of church as a community building thing now, because based off of my white friends recollection there's very little actual community around worship itself. There are a bunch of volunteer actions outside of it, but just going to worship isn't itself community. This makes me question why we can't have a generic mutual aid group do this instead, like the Anarchist Soup folks.