That’s the crux of it. How are arbiters ever going to be truly independent when repeat businesses necessarily only ever comes from one half of their arbitration? CorpoCorpInc selects your arbitration company for 200 arbitrations a year. How many of those cases does CorpoCorpInc lose before they decide to go with a different arbitrator?
So maybe if you want to make a law, find a way to break that implicit feedback loop.