Given that Uber isn't charging (and by extension isn't earning anything) on the time drivers spend to get to the pick up point, I doubt that they don't have any economic interest in doing something better than the status quo.

I think this really is an artifact of the taxi medallion system which regulates private car transportation differently depending on the way you hail it, for largely historical reasons. (Taxis that you can just flag down used to be much more profitable, to the point where a license for that used to go for more than a million USD in NYC.)