Uber didn't have to convince anyone, taxis were ripoffs. It didn't even have to always do with money. Taxis asked people where they were going and drove off if it wasn't far enough was a significant issues. Taxis not picking up black people. Many taxis in my town were dirty and and the drivers were jerks or creepy or both. With protections built into law and no competition the industry didn't have to even try to cater to the customer.

The taxi industry sealed it's own death warrant a long time ago. Ride sharing services solved a real problem at the right time. If that cost a bit more, it was well worth it. I won't take a taxi now unless I am forced to.