I haven't seen anyone supporting the elimination of existing taxi companies, other than what might happen through market competition. Most people who welcome Uber don't think that only Uber should be allowed to do ridesharing, but Uber makes most of the headlines because it's the largest player. Sometimes, I will carelessly use "Uber" to refer to the entire ridesharing-via-cell-phone industry, because it gets verbose to say Uber/Lyft/Sidecar/etc. every time.