What's wrong with the polycentric legal system proposed by anarcho-capitalists?
The premise is sound: lower the cost of changing states, and more people will be willing to leave their state when dissatisfied with its performance. This would put more pressure on all states to improve, thus effecting more efficient laws via competition. The question from that point becomes, how do we lower the cost of changing states to begin with? For this, I'd imagine legal decentralization is sufficient: dissolve the large states and leave a hundred smaller states in their place and we'd see likely see the sort of competition they're looking for.
If that's where it all stopped, I'd have nothing to say in disagreement. But they like to go two steps beyond this point, to propose first that people should have no legal obligation to fund any state (thus making it "voluntary" to some extent for some people) and that the regions served by states should be made to overlap, or perhaps more precisely that they shouldn't have regions at all (thus making it "polycentric"). It's these two ideas I'm not fond of, not because they'd be disastrous but because they wouldn't serve any real purpose aside from satisfying a few of the ancap's awkward moral theories.
Consider the first: if we let people choose not to associate with any legal or political institution, what happens? The result is everyone ends up doing so anyway, if not simply because they desire those services then because their agreeing to help fund them becomes a requirement for being allowed entry into any sort of community or place of business whose existence depends on them. The only "freedom" this enables is thus complete alienation from one's society, a social suicide so to say. And given the exclusion from such places of community or business is enforced (and will continue being enforced) just as violently as the state's routinely taxing everybody today for that same purpose, I can't see how it's morally superior to move from one to the other.
The second idea offers one significant advantage: if people could switch between agencies without changing their place of residence, which is impossible in our current system, the act of doing so would be that much less costly and the relationship between agencies that much more competitive. But this has to be weighed against the cost of increased legal ambiguity, which leads to uncertainty for the actors in the system, as it wouldn't be clear which laws are to be obeyed in which circumstances until long after the fact, once we've figured out which of those involved are willing to pay more for the privilege of the private court declaring them legitimate. And how much would that privilege cost? They couldn't know ahead of time.
It's not inconceivable that this would be a worthy trade-off, but I don't think it likely. This evaluation may be the result of some ideological bias on my end, but given I generally have no problem admitting certain aspects of other ideologies are true despite disagreeing with the ideology as a whole, and given this is an isolated topic—that is, even if my evaluation is wrong, it has no impact on any other points of belief—I'm deciding to say that there's more to it than just that.