People left the cities because of the rise in crime. Crime can always be prevented by a reasonably effective government. Read this book to get a sense of what happened in Brooklyn: http://www.amazon.com/Canarsie-Italians-Brooklyn-Against-Lib... The same story was repeating itself across the country.
Corrupt mayors didn't help, but let's not act as if this was some sort of problem that was borne solely out of poor management.