Metro service is the key. When frequencies get high enough the timetable exists only for the benefit of the operations personnel, customers don't care about it because their experience is like with an elevator. You don't ask for a timetable for the elevator, you just go to the place where elevators arrive, and wait, and very shortly there will be an elevator.

Very high densities are both the problem and the solution. They're the problem because under very high density private car ownership is infeasible, and the solution because public transport becomes fast and affordable. If you let it.