The deadweight loss is different than the overhead cost. What you're describing is the overhead cost, which indeed is much lower for a land value tax.

The land tax has zero deadweight loss, because what it's taxing is pure economic rent, rather than production of value:

https://en.wikipedia.org/wiki/Land_value_tax

Any tax imposed on anything except scarce natural resources will be penalizing the creation of wealth, and impose deadweight losses.