Yes, a ride share arbitration service would solve a lot of the problems. The question is, does Uber have enough market in enough places or enough of a name that they can resist
fully tying into a service like that.
Think Apple. They have enough market share (even if not a majority), and enough brand loyalty, that they don't need to adhere to existing standards if they think they can resist them and use that to their advantage. Think iChat, and compare to the original XMPP google chat. It was trivial to talk to gchat friends on an iPhone, but hard or impossible to talk to friends over iChat from an Android phone. By resisting making iChat open, Apple created an advantage for iPhone users. Eventually Google redoes google chat with Hangouts, and guess what? They close the protocol. Sharing is only beneficial for you if it's reciprocated.
Does Uber have the clout or loyalty to get away with this? I doubt it, especially since the bar for drivers to drive for multiple services is so low. But if the arbitration service was created without provisions to account for this (e.g., you must partake in the system to use it as a provider), it would be trivial for Uber to fill gaps in their coverage through the service while preventing other apps from doing the same with Uber drivers.