They read like Japanese cops to me. Japanese police are very friendly and helpful, and Japan has a 'problem' of "too many police officers, not enough crime", so they often have time to kill... buying lewd dakimakura covers, I suppose, like any respectable person with time to kill in Akiba.
I do like the hat theory, though. We need more yuri with hats. That's what's great about Touhou, ZUN is a creator who truly understands the importance of girls in hats.