Various non-profits, university endownments, churches and pension funds, charitable trusts and charitable foundations have far higher concentrations of cash (and by your definition, power) that avoids the tax man entirely. States and municipalities also pay zero federal taxes on profits if they happen to end up with budgets in black. If you think the (somewhat easily fungible) corporate earnings are under-taxed, what's your take on non-profits and municipals?

I am quite accepting of churches, as long as they keep their beliefs to themselves and fulfill their role as keepers of cultural heritage. Better keep them running than artificially converting churches into living history museums after they died. I would consider it a great cultural loss if, say, St Peter's would be just another ruin owned by the Italian government.

University endowments, at the scale they apparently exist, are weird indeed. Do they grow because giving money to add to the pool gives (temporary) influence over the application of the pool? That would be a surprisingly nasty scheme. A donations race like that is how the Roman bishopric originally became a political force in late antiquity/early middle ages, slowly displacing secular authorities.