Yes property taxes have another dimension of “fairness” to them, but that’s not why economists favor them: it’s because they can’t easily be dodged and are easy to extract (knowledge of property ownership is pretty reliable).

Taxation isn’t necessarily based on what’s fair or rational, it’s a way of financing public expenses. It might be more logical from the perspective of the people as a whole to tax wealth more and income less (for example) even though wealth is less logical and “fair” to tax than income or consumption.