That's true, but most people forget to take into account the cost of the car itself. If you spend 10$ in gas and vehicle depreciation to save 8$ on average on your bill, are you really winning?
When I really need to do a big grocery or to find a specific product which my local store does not have, I rent a car from one of the 5-6 carsharing stations near my place (think ZipCar), it cost me 20$ and I can go where I want. Only, I do not have to pay for a car all the time.
Schools are another topic, of course if you live in a bad neighborhood, it might be problematic, but again with a nice public transportation system, it is not an issue (in my home town, _public_ buses have specific routes for students of a given school, dropping them directly next to the school).
We can always devise a situation where you are "limited" by public/active transport ("I am an ER doctor, what should I do if I get called at 2AM on a winter night to an hospital on the other side of the town to save multiple children lives?"). Sure, in these cases, you should take the car. That doesn't mean that for the overwhelming majority of people, car _would_ not be mandatory (assuming a decent public transportation system and walkable/bikable cities).