... and thinking about it, I think the difference is this: "At home", the police already has control over the land. They have "won" almost by default. No oppon

... and thinking about it, I think the difference is this: "At home", the police already has control over the land. They have "won" almost by default. No opponent can challenge them, or have any interest in seriously taking them on. The military, on the other hand often operates where they are instructed to "win the hearts and minds" and if they don't get local support, things can go very badly for them. Which gives, it's unfortunate police not more often tries to "win hearts and minds".