I offer slightly different angle:
Human societies work best when there is pronounced division of labour. And this is also true (and maybe especially) of institutions. If you look to the past, societies thrived when there was clear division between least state and religion, and ideally when those tasks we generally associate with state or religion were further split into separate institutions. So the problem is not the size of the society, but the unification of “service providers”. Then the results are exactly as you describe. Speaking of care - most religions constantly remind their “subjects” that it actually IS their job to care, but when the church got effectively merged with state, it created the indulgences. Welfare state is just another form of this.
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