Mandating Binding Arbitration as condition of service or sale can be problematic. A contract of adhesion may effectively be used to deny people their rights in law; throwing in a biased arbitration process just adds insult to injury.
And the arbitration process will inherently be biased. Which party picks the arbitrator? Pays them and has a long-term relationship with them? Not the customer.
There are a few ways to decide who picks the arbitrator. Depending on how the agreement was written, one party may get to pick, or both parties may need to come to a mutual agreement. I recently saw one where each party picks an arbitrator, and those 2 arbitrators then decide on a 3rd party to be the final arbitrator.
So yes, the customer may have a long-term relationship with the arbitrator and may even pay them. It depends entirely on the situation. (For example, I know an arbitrator that I have used in the past and would be willing to use again.)
And the arbitration process will inherently be biased. Which party picks the arbitrator? Pays them and has a long-term relationship with them? Not the customer.