At least where I live, private arbitration is well appreciated: much faster, cheaper and reliable than the judicial system. So, yes, here I'd advocate most of the judicial system to be privatized.
Where I live (USA), private arbitration is definitely preferred by many corporations who require it, and despised by the people who are forced into it.
It's not an issue with private arbitration per se, it's an issue of being practically forced into it under unreasonable terms with no alternative options.
The fact that you can't do that with the public courts but you can with private arbitration makes it an issue with private arbitration.
Parties with fewer resources are at a huge disadvantage in either system, but there are degrees of disadvantage. It is misleading to examine the outcome of arbitration once the rules are "agreed" to without taking into account that the process of setting the rules strongly influences said outcome.
If private arbitration is not forced upon you, then there is no problem. Thus, it's not a private arbitration issue, it's forced and unappealable private arbitration issue, which is a different matter (not the thing itself but how this thing is applied)
