I think for me the biggest issue is really the insurance issue. I'm not convinced that the people providing these services are actually being covered by anything more than their personal auto insurance. And most personal auto insurance policy's have exclusions for using your auto in this type of manner, so if someone gets in an accident and has a serious injury, I sure wouldn't count on the auto insurance paying out for that. Tied in with that, I'm guessing most of the drivers for these services don't have a commercial drivers license, so they're largely operating illegally when providing this type of service (which cycles back into hence they're not going to be adequately covered on insurance).
There's nothing that's stopping uber and lyft from requiring these from their drivers, other than the drivers are obviously going to want more money to cover those costs. And cities are starting to pay attention to that and require that for these services to operate in their cities, which is probably a good thing. Whether they can still stay competitive if they have to meet some of those same rules? Time will tell.