USPS actually writes checks to pay taxing authorities. That way you don't run into the problem of a property owner neglecting to pay those taxes and the USPS finding out later that the sheriff wants to seize the building for a tax sale, and all that sort of stuff. The USPS definitely would not have its operations hindered by a property owner neglecting to pay his property taxes. First, the seizure and sale would not affect the lease under the law of any state; in my home state of Louisiana, the result would be something called a "real subrogation," which means that the lease continues as is, just with a new entity collecting the rent checks.
Look, anything that anybody does concerning a building USPS operates in ends up costing money somewhere. First of all, there's lawyers involved; then managers; then architects; then various kinds of bureaucrats. The more nonsense going on the higher this kind of overhead.
Believe me, it frequently makes sense for USPS to anticipate bad landlords and take action to eliminate cause for conflict.