But chargeback is not legally binding, is it? So you just put yourself in a situation where you received a service and didn't pay for it. I am pretty sure Uber could do something about it if they cared.
A quick google search reveals lots more, and none that I saw saying companies can’t come after you for a disputed charge. Most won’t, and most of those that do will only do it if they can clearly show they’re in the right, and you should be able to beat any collection attempt if they aren’t, but they can try.
Prime example: gym memberships