Having Axe Cop act normal feels weird. It's like making a giant trampoline to get to the top floor of a building and then using the stairs instead. But then again, even Axe Cop can't be zany all the time.
Actually, in canon he leaves normal crimes to normal cops, but since he hasn't seen any in Nexus, he's elected to take up the mantle himself. So you could say that this is a new experience for him. Not being able to just go in and chop heads off is frustrating.