Arbitration clauses don't work as intended if the company can't choose a biased arbiter to rule in their favor, so this is always part of the contract.
Uber having sole choice over the arbiter would go against my explanation being the right one. Biased selection of the arbiter is also a reason why (AIUI) such a contract wouldn't hold up in court.
I meant that the contract would seem especially unfair if Uber could choose an arbiter they didn't have to pay for.
Even if they didn't outright choose an expensive one to squash claims, it would be unfair to make an individual pay for a service they can and want to get cheaper elsewhere (on less favorable terms for Uber).
Unless there's blatant cronyism and abuse of power, I don't think biased arbitration by itself would fail to hold up. Judges are humans with personal ideologies too, so you can pick some that do everything by the book and still skew the result in your favor (especially averaged over 60,000 cases)
Arbitration clauses don't work as intended if the company can't choose a biased arbiter to rule in their favor, so this is always part of the contract.