Would you say LLCs were very largely/mostly used for non-profit purposes?
I couldn't say. Maybe the org has some firm population and firm size (1 - 1,000+) stats, maybe firm by NIC.
The key to understanding business classes here is understanding that selection is driven by concommitant tax advantage strategies and reporting requirements of each type so to shelter earning distribution -- whatever the source of income. 501(*) is a tax category of organization, whether or not incorporated, whether or not partnership, that indemnifies the firm according to strict regulation by tax agents of its business activities rather that its profit (loss) expectation. Administration is expensive. Diversity is the key to economic and political evolution.
