Many taxi companies are required to serve anyone at any time(24/7/365) for fixed prices, regardless of the cost of the trip. It is unlikely that the new transit service will steal all the unprofitable customers.
Many of the regulations around transportation are very utilitarian. There are people who can not drive and are unserved by public transportation, but will die if they do not have access to transportation. We the people(you too) have decided to contract out their transportation to cab companies. In exchange for this incredibly unprofitable mandate, cab companies get price fixing which is essentially a monopoly on many routes.