And my house is a public good, since the only reason it's not being vandalized/robbed/burnt down is that the public spends x.y% of the GDP on law enforcement
Your house, if it is like mine, is a lot more reasonably a public good than it is "private property". I didnt build this thing, will "own" it for probably 5% of its existence and do little to maintain it myself. Yeah, you are right. We owe a lot more to the "public" than we usually acknowledge.