Government is a failure with those things too (as Shane pointed out in his video response to TheAmazingAtheist), it's just not as bad as mob rule with Anarcho Capitalism may or may not end up being. The main point of this was to explore a logical fallacy (Burden of Proof) and take it from the point of "existence" to the point of "this system is better at achieving the desired goal than an alternative" as it applies to Anarcho Capitalism.
Although to be fair, a YouTuber named Confederalsocialist has made quite a few videos on private law, police, courts and defense, and on past successful Anarchist societies. The ones he primarily focused on were: Medieval Anarchic Ireland and Iceland and (believe it or not) the Wild West. Granted, they did fall, but the arguments presented were pretty good. He also goes on about Somilia and how it's far better, however he does tend to gloss over the militias acting like mini states thing (which TECHNICALLY doesn't make it Anarchist, but I digress).
As I've said over 9000 times before, however, the best arguments for private police, prisons and courts I've ever heard was from Mary Ruwart in her book Healing our World (the free online version).
Also, a good quote from Morrakiu about Anarcho Capitalism that pretty much summed up how I feel about a transition to Anarchy -
Morrakiu: "'I don't think we're at the stage where anarchy could prevail.'
I agree, but for different reasons. The only way I see a stateless society coming into being in the current conditions is through the collapse of a state, and that would make for a very painful transition during which foreign governments would attempt to re-establish a state. (A more specific version of Shane's argument about armed takeover of an Anarchist Society. Also, Shane's point that, getting a free market is half the battle while keeping it is the other half).
It has to be phased out, and that can only happen after any real or simply perceived use for the institution is gone."