Thanks for the post.

I'll chop out everything I agree with entirely and leave the points I still have questions/concerns about:
In Chapter 20, she goes into some detail on this. Aside from describing the practical methods of implementing such a system, there's also a bit to describe why the threat would be significantly lowered:
(You then printed the quote by Dr. Ruwart).
I'll have to read Chapter 20, since the specific quote you gave didn't really address my primary concern with non-coercive methods of coming up with the defense budget: Funding high-tech defensive technology against the high-tech offensive weaponry of other nation-states.
In the case of police, courts, and prisons, Dr. Ruwart introduces the idea of work prisons in Chapter 13. Criminals are responsible for not only restitution to the victim, but police and court costs as well as the cost of their own imprisonment. These costs are paid either from the criminal's personal savings (making crime very expensive, much more than what they would have gained had they not been caught) or through productive labor while in prison, such that their prison sentence is complete when their debt is paid, not in an arbitrary amount of time. It also incentivizes police to find the right person (wasting resources on the wrong person won't lead to a conviction and therefore police would not gain by trying to convict anyone and everyone).
I have to disagree with your claim that this incentivizes police to find the right person: Rather, because their source of payment relies directly on a conviction (
any conviction), it seems logical that police would be incentivized to pin the crime on whoever they can and even plant evidence. This would be especially common in cases when there's no "real" suspect in sight but when there's someone who some circumstantial evidence points to.
I see another potential problem with this as well, though I also see a potential solution. Most ordinary criminals are poor, meaning they won't necessarily have the immediate means to pay the police, the courts, the prosecutor, their defense attorney (assuming they have one...), and the prison. In the meantime, where does the money come from to pay for all of this? Lawyers and court systems might get away with subsisting on their current funds, but police officers (or rather peace officers, as they would hopefully be called again) need to pay the bills and feed their families, and they can't just wait months or years for a criminal to start paying off his debt. Who would front the money in this situation? I imagine the solution is that the court system would take out a loan to fund all these costs and then repay the bank with the criminal's money later. Is this correct?
...then again, a problem I see with this solution is that if the defendant is acquitted, the court is left holding the bag.
This also addresses your question about how a person with no family is murdered will have the case handled. And to protect the misdeeds of wardens and prison guards, criminals can have the choice where they will serve out their sentence. Some prisons may offer better amenities but will cost more, meaning that the criminal will spend more time there working off the debt.
This does
help to address my question about the lonely person being murdered, but it doesn't go all the way. When the victim is still alive or has surviving family members, would they ordinarily front money for the initial investigation and/or front money to the prosecutor? If so, the lonely person who is murdered would have little chance of being vindicated, since no one will have aggressively investigated the case to provide the prosecutor information (the investigators would rather take cases where they can be paid up front), and the prosecutor would not want to spend time working on a case with no evidence and no money up front.
Most of the arguments in this message are derived from Dr. Ruwart's work, but some of the ideas in here I've literally come up with as I write this message (like the electronic token). Given that I haven't put a lot of thought into this particular piece of the process, there are certainly flaws in it, such as the privacy issues that you mention. I wouldn't be concerned with private property owners colluding with law enforcement though. If we're taking this in the context of a free society (and it would most likely be, as roads would probably be one of the very last things to be privatized if we were moving towards libertarianism), then law enforcement would enforce the laws of a free society. That is, protecting individuals from the initiation of force and fraud by other individuals. If we have private roads in the context of today's society, then I would be very concerned about collusion with law enforcement because of the multitude of unjust laws that they work to enforce.
I think I like TheEvilDetector's idea of anonymous prepaid tokens a bit better.

Still, point taken.
If someone can't provide their own defense, and no one will provide it for them, then no one should be forced to provide for them. If you make an argument that defense is a necessity, a right, that an individual's life or property can be sacrificed for the benefit of someone else, then the logical conclusion of that is socialism; because you can make all the same arguments for why the state should take care of education, health care, food, housing, etc.
I still struggle with the idea of whether force should be used via taxation to otherwise protect the rights of individuals...after all, I'd hate to see an innocent person convicted of a crime and forced to serve a sentence (a violation of their rights and therefore aggression,
because they're innocent) simply because they didn't have money for representation and the prosecutor was "just that good." It can happen in any legal system of course, but if you don't have representation, you're pretty much screwed unless you're really damn smart yourself. As I mentioned, I recognize that from a purely principled rights-based perspective, nobody has the responsibility to protect the rights of others (just to respect them). Still, I've yet to be convinced that taking this stand in practice won't ultimately result in more rights being infringed than "legitimizing" small levels of taxation.
I do see a potential solution here, though it has a problem: As I mentioned before, there are time-sensitive problems with the "deferred payment by the criminal" solution to legal system user fees.
If the solution to those problems is that the court system takes out a loan to front the money - which is later paid back by the convicted criminal (although acquittal of the defendant raises another problem) - then this same loan could be used to pay for a defense attorney up front.
In any case, taxation for the purpose of protecting rights is a very different argument from protectionist and socialist arguments, because they argue that taxation should be used for [insert arbitrary "noble cause"], which has nothing to do with the primary (and sole) purpose of government, protecting the rights of individuals.
How are we permitting this?
My first paragraph in the above block summarizes my feelings on this best, I think.
Anyone who has had their rights violated can prosecute. Since all of the costs are paid for by the convicted criminal, the financial status of the victim is irrelevant. A prosecutor, paid by the convicted criminal, wouldn't take part in a case if he didn't feel a reasonable chance of victory. Defendants are also protected by frivolous claims with a "loser pays" system.
When the defendant is indeed guilty, everyone will be paid by the now-convicted criminal...but as I mentioned above, that raises time-sensitive concerns. When the defendant is acquitted, who pays? The victim? This may be suitable in certain cases, such as rape, where the question centers around whether a crime actually occurred at all. However, it doesn't apply to other cases where the victim was assuredly victimized, and if nobody is ever convicted, the police, courts, prosecutor, etc. all just did a whole lot of work on behalf of the victim but without any compensation. (This is no problem of course in civil cases.)
No matter what system we use (taxpayer funded or otherwise), the only perfect one is the one that has access to perfect knowledge. If someone rapes someone else in a dark alley and is able to do so while leaving zero evidence and no witnesses to the point where the criminal cannot possibly be identified, then it doesn't matter what system we have in place. The free market system itself would not be to blame for the inability to protect either the prosecution/plaintiff or the defendant.
Unless there's a way of a loan fronting money or something similar (which brings its own problems), this system actually
could be blamed for inability to protect an innocent [but poor] defendant from a slick prosecutor and a team of police with planted evidence. Similarly, depending on certain circumstances (whether prosecutors/police/investigators/etc. are ordinarily fronted money by victims to ensure the case is handled), it could possibly also be blamed for an inability to protect a poor victim, as well.
I feel that maximizing the degree to which everyone's right are respected and protected as a whole and not legitimizing any violation of property rights are interdependent. You cannot violate people's rights to ensure that their rights are not violated.
I'm not entirely sure I agree, for the reason I mentioned above:
Still, I've yet to be convinced that taking this stand in practice won't ultimately result in more rights being infringed than "legitimizing" small levels of taxation.
I'll give a very simple but extreme example to illustrate my point:
If we do not allow the use of any coercive force
whatsoever, we must also openly permit private individuals to possess weapons of immense destructive power, such as nuclear weapons. The problem here is obvious: If some old crackpot is going out of his way to obtain a nuclear weapon and spend his life savings on it (to say the least), the odds are high that he's crazy enough to use it. There will always be a few random suicidal people who just want to take out as many other people with them as possible (e.g. Columbine). This is a matter of drawing subjective lines on a continuum based on value judgments, but the unacceptable risk of some crazy guy being an existential threat to an
entire city is obviously very different in degree (if not in principle) to the acceptable risk of some crazy guy killing his family with a kitchen knife or ordinary firearm, which is offset by all the legitimate uses of kitchen knives and firearms.
If we allow people to possess nuclear weapons without taking any preemptive action, that may be respecting one crazy bastard's rights to liberty and property to an unjustifiable extreme. After all, if he sets it off and kills a million people in an instant (depriving them of their right to life), could you seriously say that the practical exercise of people's rights benefited over depriving him of his "right" to possess a nuclear weapon?
I'm not going to shy away from the fact that this is a slippery slope, since the only easily-articulated thing that separates nuclear weapons from kitchen knives is a matter of subjective scale, not principle. Still, I think it's food for thought, and it might make you question whether it's such a terrible idea to legitimize minor infringement of rights to ensure the greater overall protection of rights.