SpaceX Starlink TOS: the parties recognize Mars as a free planet
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The state isn't the only form or coercion. Given the high cost of accessing space and the extreme resource constraints, space is likely to be dominated by multinationals and billionaires.
Some forms of feudalism where serfs must pay rent for their land or otherwise starve are technically still a free market, just one where the market power is extremely asymmetric.
"Voluntary cooperation" implies options and a liquid competitive market. If your Mars colony is going to die and you ask mine for resources to bail you out, and I condition that on being the supreme emperor of your colony, that rapidly degrades.
Further, there is no reason to believe firms won't engage in straight up theft and warfare. If you just captured an asteroid that has enough rare earth metals to collapse the prices on Earth and space isn't governed by our laws, then many companies would be funding a mercenary army to take that asteroid from you.
If you were to make it so that no nation can lay claim to space, rhen it wouldn't be possible to enforce a standard of property and thus corporate claims would be empty.
Indeed, looking back at history, the State was created essentially the same time that private property was created. This is not a coincidence.
Private property on the other hand, for example the ownership of land or resources, did not exist until the creation of the state, because private property in this sense was not possible without it.
In actuality, even some agricultural civilizations didn't develop private property, and it turns out that those that didn't are also the ones that didn't develop the state.