Wrong. While there would be no one group that has a monopoly on the use of force, self defense is of course permissible. By extension you can also pay people to defend yourself. So there would be private security organisations that maintain security and ensure people and property rights are protected.
The difference is, you have a choice. If you find the police are bashing people, or holding them without trial, or locking them up for victimless crimes, you can leave and refuse to fund this organization.
The objection you will of course leap to is; what if the security organizations fight each other?
Actually, the objection I prefer to leap to is the natural tendency of markets to develop into a monopoly. This isn't a theory, it's a fact, and I could provide squillions of examples. Look at the aerospace industry these days: post-WWII there were many companies, but now there are three principle players: EADS, BAe and Boeing, that have subsumed all others. This natural tendency would also be borne out amongst these private security firms you so espouse. The simple fact is that the organisation of many private security firms into a single market-cornering cartel would be good for business; monopolies are always good for business.
Furthermore, the private donation argument doesn't stack up. If I donate my funds to Company A so that they then protect me from harm, what is to stop Companies B and C harassing me for 'protection money' as well, since I am paying nothing to them? Sure, you could assume that those who donate to B and C would have a moral obligation to cease if they found out about such activity, but who might they be, exactly? Perhaps Company B is far larger and more powerful because it receives donations from some larger entity (such as a business) who has an interest in threatening and coercing people? There is a reason that organised crime syndicates like the Mafia extort money rather than rely on charity: because it's more profitable. And this is essentially what such a private security firm would be: a euphemised Mafia.
Leading into my next point: you have a confused and blinkered belief (like most of your ilk) that economic goals = social goals. It is as though a necessary component of turning a profit is making people happy. However, this is not true, and rather than argue theoretically I will instead refer to various examples of times when private enterprise was far less regulated than it is now:
Pre-New Deal America: At the turn of the 20th century, business could do what it wanted-- and it did. The result was robber barons, monopolistic gouging, management thugs attacking union organisers, a punishing business cycle, slavery and racial oppression, starvation among the elderly and gunboat diplomacy in support of business interests. Don't think, by the way, that if governments don't provide gunboats, no one else will. Corporations will build their own military if necessary: the East Indies Company did; Leopold did in the Congo; management did when fighting with labor.
Post-communist Russia: Take Russia in the decade after the fall of Communism, as advised by free-market absolutists like Jeffrey Sachs. Russian GDP declined 50% in five years. The elite grabbed the assets they could and shuffled them out of Russia so fast that IMF loans couldn't compensate. Russia lacked a working road system, a banking system, anti-monopoly regulation, effective law enforcement, or any sort of safety net for the elderly and the jobless. Inflation reached 2250% in 1992. Central government authority effectively disappeared in many regions, although I guess you would regard that as a boon......
Pinochet's Chile: Consider the darling of many an '80s conservative: Pinochet's Chile. In twenty years, foreign debt quadrupled, natural resources were wasted, universal health care was abandoned (leading to epidemics of typhoid fever and hepatitis), unions were outlawed, military spending rose (for what? who the hell is going to attack Chile?), social security was "privatized" (with predictable results: ever-increasing government bailouts) and the poverty rate doubled, from 20% to 41%. Chile's growth rate from 1974 to 1982 was 1.5%; the Latin American average was 4.3%.
This is libertarian philosophy applied
in practise, with predictably disastrous results. But oh, wait, I
bet it was the government's fault............
When push comes to shove, anarcho-capitalism is not really even anarchism. A large part of anarchism involves the rejection of property rights ("property is theft") as being a perpetuation of social hierarchy, a cardinal sin in the anarchist world. Any "anarchist" capitalist society would have vast differences in wealth and hence power. Instead of a government imposed monopolies in land, money and so on, the economic power flowing from private property and capital would ensure that the majority remained subjugated. Therefore, how can the anarcho-capitalist idea of 'free exchange' possibly occur, since there remains a social hierarchy in place and thus a power differential?
To get really partisan and quote Chomsky:
"Anarcho-capitalism, in my opinion, is a doctrinal system which, if ever implemented, would lead to forms of tyranny and oppression that have few counterparts in human history. There isn't the slightest possibility that its (in my view, horrendous) ideas would be implemented, because they would quickly destroy any society that made this colossal error.
NB: You noted this yourself in an above post, when you suggested that anarcho-capitalism would return to a form of statism. The truth is that it would be horrendous statism. Continuing on....
The idea of 'free contract' between the potentate and his starving subject is a sick joke, perhaps worth some moments in an academic seminar exploring the consequences of these (in my view, absurd) ideas, but nowhere else."