Your reasoning makes sense, and I was concerned in a similar way when I filed my arbitration case (for about $8k) against the manufacturer of my leased car. The so called “Lemon law” in California suggests the arbitration as the first step. Surprisingly enough, I won the case, and it only took me about an hour of collecting documents and filling in the forms, and 45 minutes of the phone call.

Even though the car manufacturer does indeed pay for the arbitration, I never felt the arbiter is biased, and the judgement was completely in my favor.