The plan is that you don't get involved in any of that. All you do is provide a platform that allows customers and drivers to connect in an efficient way. If clients don't aren't willing to accept that then I guess they don't need rides.
The big problem with taxis is that they're inconvenient to use. You either have to take a chance at hailing one or call a switchboard, having no idea in advance of how long it will take to get picked up.
Uber/Lyft's platform largely solved the inconvenience problem, they could have offered it as a service to existing taxi companies/drivers without getting involved in all the regulatory issues.
And people preferred Uber/Lyft’s oversight versus the taxi services that existed before.
EDIT: Also there's a problem with the way resources get allocated. I think that platforms of this type provide a valuable service, but not necessarily one that should be considered the basis for a billion dollar business. The majority of the revenue should be going to the drivers. But it's hard to get capital for something that has no chance of creating a few more billionaires.