The drivers and passengers in these ridesharing systems are identified/tracked electronically via their smartphones. Whether or not they are displaying their corporate logo is likely irrelevant when it comes to insurance/liability. I am guessing some drivers don't put up their physically identifying logos because there have been instances where taxi drivers have harassed or beaten up drivers in ridesharing services. But as a passenger, it doesn't really make much of a difference to me whether they put up their logo because I'm relying on my smartphone to identify them.
Also, as a long time SF resident, I have had some awful taxi drivers, including some that have run up the meter assuming I am a non-resident and some that have made some very crude remarks. I have never had these sorts of problems with the ridesharing services and my experience with them has almost universally been positive. In fact, there is no meter under the control of the driver to run up with the ridesharing services since everything is precalculated, and a rating system ensures that these drivers are on their best behavior. If the taxi companies weren't so greedy with the number of medallions and there were actually enough cabs to go around during peak hours, and if they improved their customer service and modernized their dispatch systems, then perhaps these ridesharing services wouldn't be quite as successful as they are.