The short answer is that "shared resources" in a libertarian system is a bit of an oxymoron. It's a category error.
The long answer would probably be that access to these resources would be gated through pay-per-use, instead of a distributed taxation system. Of course for convenience you might end up with a structured way of purchasing a group of resources and it might even look like a roundabout way of taxation, although libertarians might argue that taxation is the roundabout way.
Or they might give a different answer, there are different schools of libertarianism!
* not a libertarian, but interested in niche political ideologies
Plus, the question of voluntary vs. involuntary comes in. Taxation is, in most forms, involuntary. Don't pay your taxes, eventually you'll either be arrested or the government will compel your bank to hand over what you were supposed to pay; either way you're not allowed to say "I don't plan to use public roads so I don't want to pay for them" or "I don't want my money going to support the military, I'm fine with the military not defending me if the country is ever attacked" or whatever. You have to pay the taxes, and your say in how they get spent is very indirect.
The libertarian ideal is voluntary payment for services. Don't want to pay for fire protection? You don't have to; the flip side of the bargain is that if you haven't chosen to pay for fire protection, the fire company is under no obligation to put your house out if it does catch on fire. The choice is yours, but you have to be wiling to accept the consequences of your choice as well.
Note that I have not studied the various flavors of libertarian philosophy, so some of them might well disagree with what I just said. But the voluntary/involuntary thing is pretty important to libertarians as far as I know, so it's definitely worth mentioning here.
Who gets to gate natural resources? Why should I recognize any power to do so? Purchase from who? Am I not free from any authority that would coerce me to accept such a system?
What's described is basically just a regressive tax. It doesn't sound very libertarian to me.
I read quite a bit of libertarian philosophy when I was younger, and never heard a convincing explanation of how you get private ownership of land, let alone things like the atmosphere, rivers, groundwater, etc.
Or pollution, are small amounts ok, as long as nobody can prove they are damaged? What if damage takes a generation, or only appears if lots of people are doing it? Diluting away the crap from burning a little oil is easy, when the whole world is doing it everybody is hurt.
Good question. Property rights are absolutely fundamental to libertarianism, perhaps second to the concept of self-ownership. Coming from classical liberal philosophy (most notably John Locke), the principle of self-ownership asserts that you own yourself, your labor, and the physical manifestations of that labor. Locke believed the earth was given to humanity in common by nature, but it required cultivation and effort to be useful. By "mixing" their labor (time, sweat, and skills) with raw land or resources, an individual removes the item from the state of nature and attaches their labor to it, making it their private property. Writers such as Robert Nozick and Murray Rothbard expanded upon this idea (Rothbard even went as far as to ground all ethics in self-ownership and property rights).
I want to ask you since I'm curious, the state simply declared ownership over territory and resources (and in some cases used violence to uphold it), why should you recognise any power in the state's part to do so? Likely many of the same justifications can apply to individuals as well.