I agree with everyone else who has said that the reason no one much uses 'public security' is not that it's logically impossible, just that it's not a normal or idiomatic collocation. I'm not awake enough to formulate a very rational explanation, but off the top of my head I'd say the question is related to why the US government had so much trouble trying to come up with a name for the new cabinet department they created after 9/11. 'Homeland security' sounds pretty silly to AE ears, like a politically correct Orwellian euphemism for 'Vaterland' with all its Nazi overtones, but 'domestic security' would have been even worse, because domestic also means household (keep husbands and wives secure?). 'Public security' might faintly suggest securing the public (tie down those protesters?), or it might sound like the opposite of private security (security guards, but this time paid for by the government?), or it might just sound too ordinary, everyday -- in fact, like a mistake for 'public safety,' which includes routine protection against, as CJ has said, all kinds of dangers.