The existence of checks and balances does not make police forces less monopolistic. The fact is that if you don't like the police forces operating where you live, you can move--and that's about it. You can't switch to another police agency at will, which is what anarcho-capitalists want.

Checks and balances are not at all absent in an anarcho-capitalist system. As I already pointed out, people who don't like the policing agency they subscribe to can end their subscriptions in a moment's notice. I'm not really seeing how rich people would oppress poor people in different manners that they currently do. Courts and law enforcement agencies have a strong stake in being fair, otherwise no one will buy their services. Why wouldn't there be checks and balances on policing agencies? People clearly have an interest in obtaining efficient, fair, and non-aggressive services (a police agency that goes around getting involved in fights it doesn't have to would see a spike in its liabilities without any corresponding spike in profits)--so is it really so hard to believe that they'd form consumer reporting and watchdog agencies for police forces? As it is, right now, you can act as a police watchdog, and while you might get videos on YouTube and stuff, you can't really force the police to change their policies. It's enough of a nightmare to try to get a cop fired--whereas in an an-cap system, all you have to do is to convince other folks to walk out on that agency and seek defense elsewhere.

Let's suppose that one rich person tries to oppress poor people living around him, by paying police forces to go after drug users, just for example. Will, firstly, he'd be blowing tons of money doing so, because no police agency would think about doing something like that, simply because it would be too dangerous. Drug users would defend themselves on their own, or collectively, with violence, and the risks of using force against drug use would rise. I think it's pretty silly to believe that all of the rich people in the world are going to gang up on all of the poor people in the world. Rich people don't necessarily get along with one another, and they're certainly competing with one another half the time.

From where does the incentive to steal instead of produce come? People clearly have an incentive to not steal, as they might get caught, or injured in the process. Career robbers would have an extremely difficult time purchasing legal much less actual defensive services, as everyone would be shooting at them or attempting to seek legal vengeance on them. Do most people in the US today steal rather than produce? Certainly not, but we fund a massive global empire, don't we?