Property taxes are not significantly different between the city and suburbs so that reasoning doesn't fly. Besides in my state (Michigan) a portion of school funding comes from the state coffers. This funding comes with strings attached as it is tied to standardized test scores. This is a devious and destructive technique to funnel more money to affluent schools and away from the inner city.
http://www.lincolninst.edu/pubs/1308_The-Property-Tax-School...