I don't actually agree with the notion that all property be ultimately the government's is an inherent part of being a functional government, as sufficient economic dependencies render it false from leading to Banana Republic incidents, as well as the shenanigans with China, but some capacity for it is vital for the functions of government to occur as there's plenty of involvement one might need in an urban center.
True, but that's not actually the principle on which eminent domain as an inherent function of sovereignty is built. It's not that all property ultimately belongs to the government, it's that the government has ultimate authority over its territory. This is something of a semantic point, but semantics are important when you're talking about government authority on the philosophical level, which is ultimately what all sovereignty-based arguments do.