How it would work in practice would depend upon the specifics of the contracts and the quality of the arbitration. There's potential for both positive and negative outcomes. Ideally competition would create an equilibrium which benefits both parties.
There's a very pessimistic, knee-jerk interpretation I'd like to address. Outcomes are in no way guaranteed to go one way or the other in this hypothetical.
Better protections for workers would allow a larger pool of potential hires. This in turn could create a cost incentive for robust worker protection and liability. Insurers may guarantee the employer or employee by screening for potential misconduct.
This is not to say that it would be a perfect system, but that there is a potential for incentives to work in both directions. With enough scrutiny by brighter minds than my own a workable framework might emerge.
The difference in this case were the criminal charges. Like in most jurisdictions in the world, it would be pretty foolish of someone to represent themselves without being trained in criminal law and court procedure — especially when a failed attempt doesn't mean bankruptcy, but incarceration.
[2] https://www.statecourts.gov.sg/cws/ECT/Pages/An-Overview-of-...
That said, a privatized law system could potentially provide greater competition and lower costs overall.
"Customary Law With Private Means of Resolving Disputes and Dispensing Justice: A Description Of a Modern System of Law and Order Without State Coercion"
https://cdn.mises.org/9_2_2_0.pdf