In order to believe that such a prohibition on firearms enhances public safety you have to believe that someone intent on committing a violent act would not do so because of the prohibition.
The government must prove that the regulation in question furthers a governmental interest. If public safety is the interest they are using then they must prove that it is furthered.
If a place is so sensitive that the government may ban all firearms shouldn't that place be protected by some type of security force?
I've never seen a guard at my local post office.