First to be clear, I am speaking in general terms. I know nothing about this case, I don't want to know anything about this case, but I have just scrolled through people's thoughts on arbitration here and thought I should offer a general alternative perspective. To be clear I'm not interested in blindly defending Uber either. So here goes...
Arbitration clauses will be found pretty much everywhere. They come under the auspice of Alternative Dispute Resolution (ADR) of which the top-three ways are: mediation, arbitration and ombudsmen.
The whole point of ADR is that:
1. there are only so many courts in a given jurisdiction and there are only so many judges in any jurisdiction, and both courts and judges tend to have large backlogs.
2. added to which going to court is expensive and time consuming. And if the other side has deep pockets and you loose, you end up paying the hourly rates of very expensive lawyers in smart shoes that the opposition employed because 600+/hour/person is peanuts to them.
So that's where ADR comes in. Its more informal, its cheaper to do and the costs side if you loose are kept under control.
Because ADR is an informal environment, this can also work in your favour. The timetable and parameters are flexible and the final agreement reached can easily be better than whatever a judge might have handed down after listening to both side's lawyers bicker.
Of course, in most jurisdictions nothing stops you from going to court first if you like. But most modern-thinking judges tend to take a dim view if you turn up in front of them without having given some sort of ADR a go first.
Is it perfect, of course not. But neither are the courts. Your outcome in court is effectively dependent on both side's lawyers and what judge you get, so you having a better outcome in court is not necessarily guaranteed !