I don’t think it’s necessarily a matter of cost rather than a matter of increased bureacracy which slows down the process and makes it harder for people to become drivers. Without knowing the details and based only on my own experience with a similar requirement, I’d expect that requiring municipal fingerprinting means you have to schedule a time with the police department, go in and get fingerprinted, have them mail it off. It’s kind of a pain and time consuming. And Uber already does a background check.
The biggest resistance to Uber, and services like it, comes from the existing industry and the regulatory corruption that surrounds it. The same thing has recently happened with AirBnB in NYC. Big corporate hotels hate the fact that it is undercutting their prices in the short term lodging market, and those big corporations already have an in with the local politicians. So they get laws that try to prevent these emerging business models through regulations made under the guise of protecting consumers. In the case of preventing AirBnB, they said it was due to problems with safety and quality, despite not being able to cite even one single case where AirBnB resulted in complaints.
The crowd sourced services market is an innovative thing which benefits consumers, and gives flexibility to providers and allows people to control their own working conditions in a way that was previously impossible.