Uber needs the network effect. Lower usage means fewer uber drivers, which means it's harder for me to get a lift, which makes me use something else. So a relatively small dip can cause a collapse un usage.
Raising prices could include raising (by not as much) payouts to drivers, which could make them more attractive to drive than Lyft. Then again, if too many customers leave, then you have a surplus of drivers who get frustrated because they can't get fares. But perhaps there's a balancing point somewhere in the middle.
And many/most Uber drivers also drive for Lyft. There's no harm in leaving both apps on and grabbing a more-elusive (but higher) Uber fare when one comes along.