In general, the rise of suburbanization has hurt American cities in significant ways. It has (though this trend is reversing to some degree in some cities) led to a situation in which the bulk of the middle class populations of cities has moved to the suburbs, leaving the cities to be dominated by fairly rich people and fairly poor people.
As suburbanization grew as a trend after World War II, the cities started to lose population. In particular, middle class families left the cities for the suburbs. The allure of relatively cheap single family homes in which to raise their children drew these people out of the cities. This trend accelerated in later decades as cities came to seem more dangerous because of things like the race riots of the 1960s.
This loss of population naturally harmed the cities. It took many productive people out of the cities. Their tax dollars were lost to the cities. Their children left the schools. The stabilizing impact of this class on the life of the cities was lost as well. This meant that cities came to have lower tax bases and more problems. The cities’ poorer populations remained, still needing governmental help of various kinds. Their children needed to be educated and their neighborhoods policed. But the loss of the middle class meant that less money was available to pay for these things. Because of these factors, many cities came to be in dire financial straits and to have trouble keeping themselves in any way “livable.”
In these ways and others, the growth in the suburban population was harmful to the cities.