If people start to actually do that, watch for that to be forbidden shortly afterwards, on some transparently bullshit pro-customer pretense.
The courts have not looked favorably on the US Chamber of Commerce and other orgs attempting to weasel their way out of fulfilling their contractual obligations.
In any case, I hope DDOS attacks on arbitration start up hard. But so far the problem has been that companies refuse to comply with their own rules. It seems very one-sided. This is something the supreme court needs to rule on.
In suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury shall be otherwise reexamined in any court of the United States, than according to the rules of the common law.
If they somehow refuse to perform the binding arbitration for whatever reason, then you have a constitutional right to take them to normal court. The Binding Arbitration system is an agreement to not go to court.
If one side of the agreement doesn't live up to the agreement then the agreement is null and void. Since typically binding arbitration is favorable to the company by way of preventing emotionally motivated massive damages judgements, aka "nuclear" verdicts (like the totally justified McDonald's "hot coffee" verdict, for instance) they are still an alright deal for the average person because they typically can resolve things quickly and effectively, and the arbitrator isn't going to just side with the company when they did something wrong.
This isn’t true for any agreement not drafted with macaroni and crayons [1].
Trivial example: you not paying your rent per contract doesn’t nullify your lease.
Severability clauses, which specifically say that nullification of a single part of the contract affects only that part, not the whole, are standard.
Points for thinking the hot coffee verdict was reasonable, though!