A huge problem with public transportation is safety and usability for small children, the elderly, and people with disabilities or who are sick. All these people often can’t use bikes or scooters. They have problems with having to wait standing and constantly out of order escalators and elevators.
I don’t own a car and live in a place with relatively good public transportation. That’s the biggest problem I see, next to how badly organised it is (at least here in Germany).