The solution to some problems is reliable public transport, and I am all for improvement, but not a solution to all transport problems.
For instance "I want to get from A to B when I want and in comfort" is not one of those problems in a large number of cases.
Public and private transport have different tradeoffs. I use both when the venn diagram of my requirements and the provision of the transport variety overlaps most.
Eg.
Car to the next town because a bus would be too slow/costly (once you own a car in the NW England busses cost a lot)
Train when I go to Manchester (faster, parking is a problem)
Train when I go to London (faster, though perhaps more expensive, comfortable, parking again)
Car when I go climbing. I don't have much gear, but I do tend to not know in advance exactly when I want to go.
Taxi when I stay out past my last train in Manchester.
You can make public transport better, but it's going to be very hard to make it on-demand, or with the same comfort level as a private car.