Except that isn't what really happens. We've been over this with uber rollout. It legitimately captures ridership from transit rather than supplementing it.
It works that way in Asia. You have taxis but really bad traffic jams drive you to subways during rush hour. On the weekend you might have a few taxi trips for shopping and going out. I can’t really comment on uber, but in Seattle they are too expensive to be considered in competition with transit, although personal safety issues on Seattle buses makes the value proposition weird.