A city center isn't required for public transportation to be convenient. I've taken public transit through suburbs and tiny towns and out to the countryside.
It just so happens that most of the public transit in the states royally sucks -- even in the city centers.
It is not a matter of quality. By definition public transport cannot connect all the dots on the map. It is simply impractical or rather impossible. The car gives us freedom of movement that nothing else can currently match. You personal anecdote of taking public transport doesn't invalidate other people use cases and needs, because what works for your situation doesn't necessary work for everyone. If I may use a CS analogy: public transport is like a collection of linked lists and a car is like one giant dictionary. Totally different use cases.
It just so happens that most of the public transit in the states royally sucks -- even in the city centers.