> You have to pay the government rent in perpetuity.

You are paying the government rent in perpetuity for the services they provide, including enforcement of your property rights. If you wish to live on land without paying government rent, you will need to go to a place without effective government. Today, that would be Syria, parts of Sudan, or Mali as examples. I doubt you want to live in those places as a 1st world resident, but if you do, there's little stopping you.

It’s exactly the correct idea. If the value of your land rises as a positive externality, it only makes sense that you contribute some of that back to the society that effected the rise in the first place.

Where I live, the government owns about 40% of the value of my labour. I have to rent my own body in perpetuity. Meanwhile my second biggest expense is a mortgage I pay for land that nobody created.

How much of the land value of your country do you currently own? A land value tax is likely to increase the amount of land you own (the profits of). I don't think US tracks land values as accurately as countries with some kind of land tax.

The alternative is unbounded compounding of wealth until all land is held by very few hands.

Paying taxes in perpetuity is what pretty much everyone does.

Not necessarily. It can be arranged so for owners with no income the tax accrues to the land and no cashflow is necessary until sale.