Not that I know of. Uber, I think, has done a good job of running a good, self-regulated, business in leu of government regulation. I'm less worried about Uber specifically than the non-medallion transportation sector in general.
Taxis are regulated because you could have issues when someone gets into a random person's car. You can imagine how that would be dangerous for consumers (both physically and financially).
I personally like Uber a lot and had a good experience when I was able to use them. But, you could see how a lesser competitor could cut corners in background checking their drivers.
I'd rather have somethings explicitly regulated than trust that all companies are interested in spending money on things like background checks. AirBnB has the same flaws, but even more pronounced.
