While I agree with your post and the premise behind it, I do believe that Uber has the potential to make a case for themselves as a "social networking" type of application as opposed to a car service.
How long do you have to know someone before you're allowed to give them an "insured" ride in your own personal vehicle? What if you go to your first day of College/University and meet a classmate who happens to mention they're taking the bus home, so you offer them a ride? Would they not be insured? Of course they would.... well, what if you met on a phone app? What if you met on a phone app, say 5 minutes before you were in an accident instead of 5 hours?? Where is the line drawn?
Most people would apply common sense to that point, as I am sure that's what you are doing... but I do think Uber at least has a shot at being off the hook in terms of insurance.