Right, but this is a minor subset of your initial premise. And even in that subset, outside of water/mineral rights[1], you are talking edge cases. A road is a quasi-public-good until there is a traffic jam. Central park is a quasi-public good until it is occupied by a permit holder, etc.

Second, The public policy rationale for these "investments" is to provide quasi-public good as services. For example, the public ownership of military installations is not a "public good" in terms of property (you cant take a walk at area 51) but defense is a quasi-public good (avail at ~zero marginal cost to the broad public).

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Its important to just keep some perspective. Public goods and "profitable investments" (eg, rent seeking ones) are quite distinct concepts. And in part we entrust assets subject to massive rent-seeking to be held in common ownership "for the public good" expressly to avoid exploitation their rent seeking potential.

[1] The exploitation of water/mineral rights relating to public land are often well trodden areas of legal and policy debate, and span levels of abstraction (state/local/regional etc).