> For instance, imposing a very high land value tax would reduce the value of land, which would in turn reduce the cost of housing.
It would only potentially reduce the tax-exclusive cost of housing. It would not reduce the tax-inclusive cost. (In fact, the rational expectation would be that it would radically increase the tax-inclusive cost.)
It would not change the tax-inclusive cost of housing. Land taxes can not be passed on.
You are right, that the tax-inclusive cost of housing won't change with a land tax on its own, at least not as a first order effect.
If however, you eg use the land tax proceeds to lower taxes on labour and capital, building higher (ie using more capital for housing) will become more economically feasible. (No economic revenue will be lost. Lower taxes in a jurisdiction directly lead to higher land prices---which the land tax will capture.)
It would only potentially reduce the tax-exclusive cost of housing. It would not reduce the tax-inclusive cost. (In fact, the rational expectation would be that it would radically increase the tax-inclusive cost.)