Not true, Uber can be 40-60% cheaper. I've stopped taking public transit in the Bay Area because of Uber, I don't think I could do that with Lyft alone. Is there another competitor with cheaper pricing?
I don't know about the US, but in India, Ola offers cheaper prices than Uber (about 30 - 60%) and people are switching to it. Uber hasn't been deleted, but it's losing customers (at least the ones using cab services regularly) to Ola.