No - it's not possible to avoid. However, arbitrators aren't robots, if claims are being filed in a clearly malicious or frivolous manner you can expect a level headed mediator to provide a remedy.
In a case where one million people were legitimately harmed though, this can be absolutely disastrous for the company unless the wronged agree to waive the arbitration clause with the company and pursue something like a regular class action lawsuit. It'd still be more expensive than a regular class action lawsuit however.
What? Just go read the PayPal one. It says very clearly you can only bring arbitration cases on an "individual basis". Which was directly in response to this issue.
"Unless both you and PayPal agree otherwise, the arbitrator(s) may not consolidate or join more than one person’s or party’s claims and may not otherwise preside over any form of a consolidated, representative or class proceeding."
Edit: maybe PayPal was the wrong example here - I definitely saw clauses change after the Uber court case, but it seems the PayPal one had been there longer?
That doesn't make PayPal immune to being overwhelmed by arbitration requests, it just requires clients to file separately (which they generally should be doing anyways).
That means that multiple arbitration cases cannot be joined together - which is actually worse for them, as they have to pay a fee per case, so more cases means more fees to be paid.
In a case where one million people were legitimately harmed though, this can be absolutely disastrous for the company unless the wronged agree to waive the arbitration clause with the company and pursue something like a regular class action lawsuit. It'd still be more expensive than a regular class action lawsuit however.