Uninsured motorist protection. i.e. you get hit by a driver with out insurance.

I don't see how this could be. Uninsured motorist protection for my wife is $22/6 months and $19/6 months for me (older car). Compare that to $130 and $120 for liability. It would seem that I am much more likely to run into someone than it is for someone who is uninsured to run into me.

Your liability coverage has to be able to cover you doing significant damage to basically anything or anyone else out there on the road (potentially something really expensive), and probably includes some coverage for you being sued by the owner of whatever you hit. In contrast, the uninsured motorist protection is not only relatively unlikely to kick in for any given incident, it only has to cover your particular vehicle, and is probably actually subsidized by the rest of your premium.