Especially when the tiny blonde cop successfully tells the gruff off into leaving.
The main reason why I might think certain public areas might be declared ANT is to do with essentially declaring certain areas off-limits to proprietary claims - essentially, we're calling this place neutral, because otherwise there's too much risk of factions fighting over it. Given the power of faith and emotions in the Dresdenverse, I suspect a lot of places of power would actually be public landmarks, charged up by many visitors sharing an emotional context - as such, even covert clashes might pose a risk of exposure. It would make more sense for some areas than others, but some might use the ANT clauses to forestall that.
Plus, even supernaturals can feel civic pride and want their locale's special places to be recognised as such, including by outsiders.