a) near zero latency to take a trip I can take the subway and go home at any station. If I go by car I have to go back to the place the car is to be able to return home.
b) proportional penalty for leaving late: if you miss a bus or a train by 10 seconds, you have to wait for the next one, which can be an hour. This is true if you favor private cars over public transportation. The more people uses the bus, the more buses there are, and they come more often (in rush hours you can take a subway each 5 minutes). The problem solves itself.
c) availability: a personal car generally provides the same service during the day, at night, and can be used in rain and mild snow (heavy snow, if properly equipped). Yes, at night there is less public transportation. But at night there are no "traffic jams" either. When your needs are completely different that the rest of the population then a private car makes a lot of sense. This should be the main use.
d) flexibility/directness: a personal car can drive to almost everywhere, and can generally take a fairly direct route. But usually, people don't want to drive everywhere. Most people wants the same route that everybody else. That's why you have "traffic jams" in the first place. It is the same case that c), if your needs are so different that the rest of the population a private car makes a lot of sense.
In all cities I have lived (Barcelona, London, Stockholm) by far the best option was to use public transportation.