A credit card chargeback should be used as the last resort, and for good reason: many service providers will permanently suspend your account if you do one.

There's typically a thread or two per year where some poor sap gets double charged by Google or similar company, uses a chargeback and then gets their entire account suspended. Poof, all your mails are now permanently gone.

So yeah, only do it if you're OK with never using Uber again.