It's not a "sense" of community that's lost, but actual community.
> Secular movements to restore a sense of community would be welcomed IMO (there are articles about how local mcdonald's have become gathering places in small american towns, surely this isn't ideal)
Because there are no communities, there is nothing to organize or coordinate that can possibly hope to raise the very substantial funds that would be necessary to operate a public building.
Really, this kind of thing should be tax-funded, like libraries often are. Organizing that way would be easier and more sustainable, yet still seems hopelessly far out of reach.
Churches manage to live from "tithing" donations which requires deploying a very complicated mental infrastructure to keep people so willing to invest so much. The idea of manipulating enough people in some way to cause them to forward so much of their income to a secular community center seems also hopeless.
Outside libraries, America doesn't have indoor public spaces, "third spaces." Except for whatever businesses might set up as their little hooks to get sales -- probably short-lived since a faux community built on a semicovert sales strategy isn't easy to develop either.