Re: egg and chicken much?

If you are suggesting that it's possible to have a class-divided system

I don't support a class-divided system. I support social mobility. Yes, I support inequalities created by individual social mobility, but by definition social mobility implies breaking class barriers. And yes, I admit this happens too few times in any developed country today.

I shudder at the thought of how order would be enforced

Community level defence forces. They have proven very successful in countless guerrilla movements around the world, but have either been defeated (the Paris Commune, the Spanish Republicans) or, if winners, been converted or absorbed into state forces (Cuba, Occupied Palestine).

and how laws would be made.

Except for a Constitution and the common agreement on a system of arbitration, all laws can (and should) be as local as possible.

Obviously, the capitalist class would have to do these things themselves in a direct sense rather than establishing a state to do it for them,

What you told Goethe:

What if workers disagree with you? What if they seek help from other people who will sympathize with their desire for freedom and who do not agree that lack of capital is the social equivalent of an ownership tag? Without your so-called enemy, the state, to back up your claims of ownership, your claims to control workers will have no teeth whatsoever.

with privatized police forces that people would have to pay out of pocket in order to receive protection from,

1) In monopoly, I don't see how that is different from what there is now.
2) If multiple providers were allowed, they'd have to supply better quality or better price or both. Current police forces don't.
3) Again, community defence forces.
4) And, see below: free rider problem (or advantage, if you're the free rider)

and in such a case, the capitalists would truly be the law.

Without the state to back up your claims, your claims will have no teeth whatsoever.

And prisons would be entirely privately owned, thus insuring a large amount of detentions at the behest of the capitalists.

I don't support prisons, except for kidnappers. And even then, rarely.

I can just imagine the new types of insurance companies that would emerge under such a system, which include insurance for police protection

Not really. Private policing has a huge free-riding problem. A criminal has no way to know whether or not you have a "policy" (for a lack of a better term, but I know what you mean) before attacking you. And arguably, neither does the officer who would defend you. But still they'd have to defend you 1) just in case, so you don't sue him, and 2) because it is likely the criminal didn't just commit their first offence, or if they did, would've done it again if left to get away, either of which impact his future pay/profit.

and sanitation,

If people in developed countries paid what sanitation really costs, maybe they'd have more environmentally friendly habits.
And if people in developing countries found themselves outpriced, maybe they would develop local (and again, more environmental) solutions instead of relying on governments which are too poor, tech-defficient or lazy not to just dump it all in the nearest lake.

people had to pay directly for water,

All the more so! Funny that all the ancient civilizations began in places with lots of fresh water, and not in, say, Las Vegas

There is a reason why Saudi Arabia and the Emirates are ahead of the West in water infrastructure technology, you know?

and no more encouragement to form charitable institutions to help the poor.

How exactly does the state encourage this? And please don't mention tax exemptions, because it's easy to show this is both inefficient and regressive.

And then the less fortunate workers would miss the days when they paid for essential services out of taxes rather than having to pay for all of them directly out of pocket, which would take up 80% of their meager paychecks instead of just 20%.

Then how is it that most of the government expenses in any country go to operational expenses? (Departments may vary: the USA spends an unusually high amount in Defence, of course. But also, suprisingly, on health. Other countries spend more on entitlements and on debt. In any case, operational expenses always exceed the actual cost of the programs)

Before I am accused of putting words into your mouth, I am not going to assume that you would prefer what I described up above to the existence of a state,

Of course not. As I have said, several of your assumptions are wrong about me.

but if the state was entirely eliminated within the confines of a capitalist system,

If you mean the kind of crony/cartel/collusive kapitalism there is today, then the state simply cannot be eliminated without the system falling. The state is a compulsory requirement of such a system.

I am NOT advocating for crony kapitalism, never have and never will.

I am wondering how you would expect people to receive essential services such as police protection, sanitation, health care, water,

Replied.

Oh, in some cases there might be natural monopolies that allow for a quasi-public enterprise to exist. In that case I would favor the shared property of the enterprise by the whole community, under a charter specifying that the enterprise has to operate as it would under market conditions and never turn out a deficit - however, with both some leeway in pricing policies (so they can be progressive) and with a duty to return profits to the citizens (Brunei, Alaska).

Police is certainly not going to be this case; health is only going to be this case in small or isolated communities.

court trials,

Case by case arbitration.

Arbitration has always been cheaper than courts. And more trusted, in the societies that use/used it more.

A court should only act as an appeal against an arbitration that is not leading anywhere, and in that case the party that calls it should bear the larger share of the costs.

Judges should have a Law degree and should be agreed to by both parties (including the fees), but should not be allowed to set precedent in an interpretation that expands a law's scope (although they are allowed to rule so).

Since arbiters are chosen by the parties and only binding because of mutual good faith, I don't see any special requirement that they have a Law degree or are "professional" arbiters, although many plaintiffs will surely prefer them to be. Obviously, an arbiter's decision cannot set precedent.

and other services if all of these things became entirely privatized and run for profit.

Well, all I have described can be run for profit without pauperizing people.

And if businesses became entirely unregulated, who would bail them out when they went broke or messed up,

Nobody.

That is crony kapitalism.

If your business fails, tough luck and thanks for participating! If it was your money (or your credit) you invested to begin with, then the losses are yours too, not everyone else's! And least of all by force of law! (if you have a rich uncle, well, you were not that unlucky after all!)

If you know you're going to be bailed out, then you know you're never going to lose, therefore you can take any risk in the quest for any additional penny, because, after all, you're bailed out if the risk wins. This is exactly the incentive for the worst abuses the capitalist system has brought about: all the wins are mine, all the losses are public. How can you not behave like a gambling addict when you know every card pays?

And what part of I support social mobility is unclear?

and who would guarantee fair labor practices, including the end of sweatshop conditions,

Sweatshop conditions are no longer necessary in any industry except mining and high seas fishing. Perfect labor mobility would grant that employers with the best working conditions always hire the workers, either killing employers with worse labor practices or forcing them to improve them.

Of course, this is impossible if there are restrictions on labor by place of origin, because then you have a pool of prisoners of borders that cannot work for a company that offers them a better deal because that company happens to be in a different country.

and who would take care of the people who these all-powerful capitalists chose not to hire

You have your stats wrong. In every country, even China, small businesses account for a clear majority of private employment.

You should be more worried for bureaucrats. In developed and nominally socialist countries, the government accounts for about half of all employment.

(since money would be even more essential to have then than it is now)

you already saved in taxes and in cheaper credit.

when there would no longer be any impetus for charitable institutions?

I still don't know where you pull that from

There is charities in Iraq as we speak, and all through Hussein and then the invasion Same thing in Afghanistan: civil war, Taliban, invasion, new government, new civil war

If what was happening in Iraq and Afghanistan is not a strong disincentive to charity, I don't know what would be