I would conjecture that Uber constantly being under attack (i.e. having lots of negative articles about them) has played a significant role in this. So when people have to pick between Lyft and Uber, they go for the one that seems "less evil". Perhaps the reason Lyft doesn't come under fire as much is because they haven't grown enough to divert attention from Uber?
If we consider the long-term outcome, is this actually a problem for Uber? If you move between places where both Lyft and Uber are available, and places that only have Uber, it doesn't seem unreasonable that you'd just stick to using Uber. But anyway, once you have an account with one of the two services, what incentive do you have to create an account with the other one?