I should have "democratic legitimacy". Rich institutions evading taxes to do philanthropy is form of privatization the people didn't necessarily sign up for.
You can have both, just be the former royal ruling house of Bavaria. They managed to et a law in 1923 that tranferred most of their property into a public foundation, outside public control. Basically, they got to retain the majority of their properity without any strings attached. Law is still upheld and defended by Bavarian parliament. Heck, they even have the right to live in parts of all the famous Bavarian castles. Also, this foundation is owning 12,000 ha of forest. All of that in addition to the stuff they privately own.
Well, at least the results their were explicit in the law --- the representatives of the people were directly consulted about the matter at hand. The phillanthropy-privatization process elsewhere is quite subtle and I am not sure many people have followed it end to end.
Well, in 1923 t was more a deal between the king deposed by the 1918 post-WW1 revolution and conservative politicians. Since then, well, it is something we Bavarians don't talk about much. It basically is a state-funded, oversight free way to pay stipends to the former Bavarian ruling house. For longer now than the Bavarian kingdom ever existed.
The Wittelsbacher family got of easier so, than the Habsburg rulers (they lost everything, Austria even went so far to abolish every single noble title) and the Hohenzollern of Prussia. I guess it helps not being in the main crosshairs of the Entente back then.