Yes, people should drive cars to work if it is their only way of getting to work. If people live in rural areas, there is often no public transportation. Alternatively, there is no efficient way to use public transportation, and what might be a short ride in a car could turn into many hours on an inefficient public transportation network.
People should most certainly drive there cars to work. In some areas, cars may only be one option of many, but to some people, commuting by car is the only option. Not every town, city, or municipality offers public transportation and some people have to travel large distances to reach their place of employment.