Network effect usually implies some kind of lock-in. Unless Uber is willing to go exclusive and qualify the drivers as employees, getting more drivers out on the road also means getting more Lyft and Gett drivers on the road, as most will just have multiple apps running.
It's hard to switch between apps. I've asked all my drivers the same question, and they all say that it's more trouble than it's worth because at least in the Bay Area, there work is constant as an Uber driver.
I feel like almost every über I see has a lyft sticker too. The UX of switching apps seems like a minor inconvenience given that most of them use waze to navigate anyway.