We already have private police forces. (security guards, police in private communities, etc.) On a different note, we also have privatized prisons. With re prisons people tend to not like them because of the incentive to keep people locked up. I don't see how privatized police forces would escape the same kind of criticism.
The customer of privatized police forces is you, the end user, which is why there is healthy competition and relatively few "incidents."
The customer of the privatized prison is not you but the state. As a result, they compete with each other to do the best "prisoning" (ie punishing bs rehabilitation, using them as almost-slave labor) for thirst cost. If you were the customer, (as in you directly picked your prison provider), the incentives would be much different:
http://youtube.com/watch?v=SzYJYSm-MfI
I think the reason there are fewer 'incidents' as you put it, is that private forces are wont to escalate issues to state police forces. Some private security have severe restrictions on when they may or may not fire their firearms --due to not having the same immunity (indemnification) as state police forces.
The video presenter presumes people will follow rules --even violent people will follow rules --what force is going to enforce those rules 'not being on someone's property', for example. And unless all communities are run similarly, this will create 'outcasts'. Bad actors would just find another place to lay low.
All types of prison systems have that incentive. Just because government prisons are non-profit entities doesn't mean the people running them don't make out like bandits. I've read that the California prison guard union is politically very powerful.
Private police, though ... in an era where early death is relatively uncommon vs. omnipresent, what's their incentive to take risks beyond what they're paid for? That what can be problematic, there's many reasons self-help is outlawed, but in the examples you give there's no immediately obvious problem.
I think the issue with regard to privatized prisons (and perhaps would-be privatized police) is that there's a profit motive. A need to keep profits up. Whereas public prisons can take the hit --ie. the losses are incurred by state coffers. A private corp can't take that economic hit as well.