One of the issues with projects like this in the US has been classism.
This may not seem to be an obvious analog, but consider public transit: state subsidized mass transit is particularly useful and necessary to those who are poor, and have trouble affording their own transportation, thus adoption of public transit tends to skew towards lower income levels. Consequently, public transit becomes associated with poor and working-class people. People in higher classes who are classist start avoiding (or never adopt) public transit because they don't want to be around those people – unless they're provided with their own separate transit system.
Thus, one of the answers to the question "Why didn't Google, Apple, etc fund improvements to the San Francisco Muni or other public transit service, rather than running their own buses for their employees" is "If they did that, their employees would have to share the ride with all the sorts of people who use public transit."
The same problem should be anticipated to arise in such a "community kitchen" project. Indeed, what makes the "community kitchen" idea novel is the "not just homeless" (nor, presumably, impoverished and hungry) people part, because that's the only thing distinguishing it from every other soup kitchen in the US.
Remember, we already have food being given away for free for anyone at all who presents for it. But only desperately hungry people avail themselves of it, because most people object to the company they will have to keep to do so.
Is the "community kitchen" in the series you watched, perchance, a Langar? Maybe the world-famous Langar hall of the Golden Temple? Because that's not merely "the local religious organizations", that's a religious practice of the Sikh religion.
That's an important specification, because India, too, has legendary classism – casteism – and the Sikh religion preaches against it and for the radical egalitarity of all people, and the Langar is for the purpose of expressing Sikhism's anti-caste, radically egalitarian principles. It is the point of the enterprise that people of any and all castes sit on the floor together, none physically higher than any others, and break bread together. This, in a society where there is actually a concept of "Untouchables", is a politically radical act.
When people go to the Langar hall of the Golden Temple to eat, they know they are going to a cross-caste, multi-class gathering in the name of the fellowship of all humankind. That is its whole point.
If we're talking about a Langar, the fact that it's not some vaguely specified "community kitchen", but a religious activity specifically organized to confront classism as an expression of religious ideals of egalitarianism is in no way incidental to its success. To whatever extent the Langar succeeds in its caste-rejecting project and attracts people across caste lines – and I don't know how successful it is or isn't in that – it's not an accident.
If you are going to want to do that in the US, and not just run another soup kitchen, you're going to have to find a way to promulgate the principle that the purpose of the gathering is to have people of different classes break bread with one another. Since classism in the US is radically taboo to mention, in a way that casteism is not taboo to mention in India, I have no idea how you would do that, or what religious or cultural organization would have it in their mission to take on such an anticlassism project.
I don't even know that, put like that, you'd still want to do it.
If you do, it would probably be very edifying to investigate the Golden Temple Langar, to study not just how to make enough dal to feed thousands of people/day, but to study whether their thousands of guests are as representative of the diversity of local Indian society as the Langar aims to be; to study not just the sanitation challenges of mass food service, but how the Langar communicated to its non-Sikh guests what the purpose and expectations of the event were, and how they convinced non-Sikhs to participate; to study not how to coordinate large volunteer efforts, but how the Langar handles it when someone misbehaves at the meal, from a Brahmin getting snooty about a Dalit, to someone with a mental illness having an episode of uncontrolled behavior, to members of two rival gangs/clans encountering one another.