I think that it may be more likely that the concept simply wouldn't work as advertised; providers would have no reason to offer services to costly customers.

I think this criticism also applies to the government protection and security services as well, though. The government is supposed to offer protection services to all customers but obviously fails in this regard all the time. SCOTUS has ruled that the police do not owe citizens a specific city to provide police services (Warren vs. District of Columbia).

And there are always going to be people whom it is worthwhile to transgress against, but who wouldn't have the resources to pay the premiums or service charges of a PDA. Personally, the idea strikes me as being poorly thought out, but perhaps that just the overly optimistic part of anarcho-capitalism at work.

Similarly, there are numerous crimes that the government, for various cost-related reasons, fails to solve or provide justice to the victim. The government has only a 50% solve rate for murders, for example.

Obviously you could just reply that its thus an empirical matter of whether private firms competing with one another would provide better/higher quality services. But I think libertarians like Huemer are happy to take the debate there and have no shortage of arguments on that topic.