Actually yea - I can't deny that your proposed person is pretty likely to go into policing after serving in the military. But I do think that people with a strong sense of civil service would also be likely to follow that path, people (generally speaking) aren't going into the military for glory - a lot of folks do it out of civil obligation and another large slice is there since it's a good way to get some economic mobility.

That said, yea, glory hounds would make really scary police officers.