I'd be shocked if any significant number of UberX and Lyft drivers had a CDL. Even in NYC, where a TLC license and commercial insurance is required, drivers still don't need a CDL.

Some driving definitely requires specialized skills, but driving a Prius around SF or $random_american_city isn't it. Autonomous vehicles have gotten quite good, and I can easily see them filling the taxi/Uber use case by 2022.