Natural rents cannot be eliminated; they must always accrue to someone. From the point of view of economics, it does not matter who.
If they accrue to an owner-occupier, he can spend them on himself. If they accrue to a landlord, he can spend them on himself!
If they accrue to the state, it can spend them on what it likes. Once essential expenditures are taken care of (costs necessary to preserve the income stream: security, infrastructure, parks...), there will be a large surplus. In an ideal society, much of this would be spent on beautifying the area. Pavements would be made out of brick, maintained in perfect condition, washed daily; bins would be polished and emptied regularly; there would be no litter; gardens and planting would be immaculate; buildings would be given new façades.
It doesn't all have to be spent on space travel and welfare.