Uber still has the most drivers and the cheapest prices.
Even if I were entirely selfish it wouldn't be in my interests for them to be stressed and rushing to cram in as many jobs as they can.
This is why I don't get why Uber tries to "undercut competitors". Even if they succeed, the second it stops bleeding money and raises prices competition will reappear. It's not like it is hard to install another app.
People spend money on that sort of thing.
That aside, getting drivers is half the battle; even choosing on a selfish basis (and I choose ride-share services on a selfish basis) - if you have more drivers, I have to wait less. For a while, in my area, lyft consistently had more drivers and got there quicker, while uber was consistently cheaper; when I was in a hurry, I'd use lyft.
(my perception is that this has changed and that lyft no longer has that advantage in my area, but point being, if you can't get there in 5 minutes and your competitor can? I might be going with your competitor, even if it's more expensive.)