Weren't communes in Israel quiet successful?
I have one followup question, and one challenge of the assumptions of the question. The followup is, how much do we actually know about the social organisation of, say, 2000BC Britain? We can dig up their pots, but that doesn't tell us whether the kiln (much less the land) was communally or personally owned, or whether they even conceptualised ownership in a way we would recognise.
The challenge is, what do you mean by 'flourished'? Subsistence agriculture means grinding poverty. I would suggest that you need a metric for success, and some specific examples of cultures known to have organised themselves communally for a long period; then you can investigate their flourishing (or otherwise) by the metric you defined, and the reasons for it.
I wonder if the modern notion of a commune vs private ownership is even stable enough throughout history for this question to be meaningful. Heck, don't you need some notion of currency/economics/property rights to distinguish between a hired hand and a member of your commune?