SpaceX got contracts to launch a couple of GPS satellites for ~$80 and ~$90 million, compatible ULA launches were in the military budget for ~$420 million.
It’s not like buying a bus ticket so pricing is complex and difficult to compare but spacex is all around dramatically cheaper than the competition.
SpaceX launches are way cheaper than competitors already. More competition would drive costs further down but it very much already exists.
A SpaceX launch costs 5% per kg of what a space shuttle launch cost. A 95% discount is pretty far away from “doesn’t reduce customers cost”.