Both collecting and disbursing rent improve how we treat Earth. Collection motivates greater efficiency by resource consumers. Disbursement lets people engage in less work, an activity that is resource-intensive. Less consumption of sites and resources spins off fewer byproducts, e.g. pollution. And as revenue from a tax on pollution would fall, revenue from a fee pegged to land value would rise.
Land value is a near perfect metric of the health of a society.
As conditions improve, more people are drawn in, pushing up site values. There being fewer residents to share rent lets the CiDi hover around a comfortable level. The local city, the most intimate government, could handle the rent of residential sites. The local county or shire could do agricultural. And finally the globe, the least intimate breadth of government, could handle rent from oceans and geosynchronous orbits.