To have one without the other? You mean pubic funded fire brigades that are managed by a private company? Yeah I can see that. On the other hand though, I see a lot of problems with a privately run police force. For example if the chief of police was making a profit from fighting crime, why would he not expand his business by creating more crime to fight?

What criterion do I use to say the government shouldn't make twirly straws but should collect tax for (and possibly run) fire brigades? The nature of the service and how fundamental it is to society. Also a strong consideration should be put into the negative effects that personal interests can create. If the only drinking straw company decided it was going to make gold straws, poor people wouldn't get any- but that wouldn't be such a big deal. On the other hand if fire brigades were run for profit and have private interests- poor people's houses would burn to the ground with fire crews doing nothing but maybe toasting a marshmallow over the flame. Even worse, maybe when business is quiet, a fire station may light some fires.

This may sound a bit vague but like I said I think it's a concept and not an actual system. The concept I subscribe to is that the back bones of society should be funded and maintained by the government. In some cases, This maintenance can be subcontracted out to private companies rather than micro managing- but not always (not for police for example). Any further than these fundamental social services is most likely going too far and will have too much of a stifling effect on the economy.