This book offers some of the most cogent arguments for anarco-capitalism, so I want to give a brief illustration of what an Objectivist counter-argument would look like.
(For the uninitiated, Objectivism is a philosophical system that agrees with libertarianism on some points and disgrees on others. It's difficult to summarise all of the differences because modern-day "libertarianism" is quite a vague term. However, Objectivism is definitely opposed to the anarcho-capitalist wing of the libertarian movement. For the curious, [1] is a good basic introduction to Objectivism, and [2] contains a slightly more technical introduction.)
Page 62 of David Friedman's book:
> In such an anarchist society, who would make the laws? On what basis would the private arbitrator decide what acts
were criminal and what their punishments should be? The answer is that systems of law would be produced for profit
on the open market, just as books and bras are produced today. There could be competition among different brands of
law, just as there is competition among different brands of cars.
> In such a society there might be many courts and even many legal systems. Each pair of protection agencies agree in
advance on which court they will use in case of conflict. Thus the laws under which a particular case is decided are
determined implicitly by advance agreement between the protection agencies whose customers are involved. In
principle, there could be a different court and a different set of laws for every pair of protection agencies. In practice, many agencies would probably find it convenient to patronize the same courts, and many courts might find it
convenient to adopt identical, or nearly identical, systems of law in order to simplify matters for their customers.
It's precisely this point that every pair of protection agencies needs some kind of prior agreement that prevent normal market dynamics from applying to dealing between protection agencies in such a system. In normal markets any firm is free to walk away from any deal with any other firm, and find an alternative. This freedom to walk away and find an alternative offer is what gives both sides negotiating leverage.
This might be difficult -- if a startup makes iPhone apps, they will find it difficult to avoid dealing with Apple, but they do have options -- they can switch to making Android apps, convert their apps to purely web apps, petition Goldman Sachs to fund the next generation of iPhone-killing smartphones, and so on.
However, if Bob's Local Small Town Protection Agency (with 50 employees) is signing a deal with WalMart Mega Protection Agency (with 2 million employees), Bob has to agree to whatever terms the WalMart agency sets. If he does not, if there is ever a conflict between one of Bob's clients and one of WalMart's clients, the WalMart agency can simply send their vast army over and force Bob's agency to submit. Assuming that Bob and WalMart both realise this when negotiating their deal, both will also realise that Bob effectively has to agree to whatever terms WalMart sets.
The takeaway of all this is that it is not logically possible to have a system where "every chooses their own 'brand of law'". The reason is that since anyone can hypothetically interact with anyone else, whatever legal system you choose to adopt will have to "interface" with every other legal system, on terms that are ultimately set by naked force. Or: no matter which "personal legal system" you choose, you're locked into the same "meta-legal system" as everyone else, one with a very odd structure.
One million scientologists demand that anyone who criticises scientology be heavily fined? You have to pay the fines, unless your agency is able to fend off the scientologists. One hundred thousand Salafists declare that they will kill anyone who criticises Islam? Unless your protection agency is able to shut them down, you have to remain silent.
(The logical endpoint of these dynamics is that everyone subscribes to a few very large protection agencies, and anarcho-capitalism ends up looking something like medieval feudalism, where everyone ultimately relies on a few powerful "dukes" and "kings" for protection.)
> In such a society law is produced on the market. A court supports itself by charging for the service of arbitrating
disputes. Its success depends on its reputation for honesty, reliability, and promptness and on the desirability to
potential customers of the particular set of laws it judges by.
This creates an enormous incentive for protection agencies to covertly lie, smear, and destroy the reputations of competing agencies via whatever means available.
[1] https://theobjectivestandard.com/what-is-objectivism/
[2] https://objectivismindepth.com/introduction-to-objectivism/