Obviously, there are major issues in "ownership" of a river. Like the air, or the open sea, it's something that is a natural commons, and there have to be laws on that.

So what if some idiot blows up all the fish in his own lake? Is this likely to be any more common than someone who routinely burns down his own house?

I have no problem with pollution laws, or any others that involve one's actions directly affecting someone else's property. The problem nowadays is that the "effect on the general public" bar is so low that they've had to dig a ditch for it. A clever socialist can figure out a way that any conceivable action of yours somehow "affects" the public. It's how the term "interstate commerce" got stretched so far out of shape.

A resource is only as valuable as the investment required to exploit it. Without mining companies, capital, technology, and human skills, all the ore in the world makes no difference to those sitting on the land.

Laws have been created to try and quantify ownership in things like this when ownership has not been established any other way. Under these laws, ideally, a miner can establish ownership of a claim by exploiting it to a certain level. In recent times, it's just been easier to assume the government owns everything, and politics decides the rest. Look up what mining and grazing rights typically cost, and what incentives would result from that.

The government is typically pretty shitty as a commercial property owner. But why bother? It's not like they need to make money at it like a private owner would.