The only two cities in the top 10 that I didn't mention (Miami, Florida, and El Paso, Texas) haven't had Republicans in office either -- just Democrats, independents or nonpartisans.I was rather surprised that his definition of non-Democratic leadership doesn't include independents and non-partisans.
Of course, there is a reason why Republikans rarely rise to power in traditional cities: the GOP has nothing but contempt for cities. National Democrats aren't exactly great either, but Republikan urban policies almost exclusively support raiding the wealth generated in major cities and transferring it to Republican jurisdictions. Oh, and putting city residents in jail for non-violent crimes.
Beck also seems to put a great deal of city's problems on their shoulders. While certainly city governments are far from perfect, they also have rather limited means to solve their own problems. A few cities, like New York, Chicago, and perhaps even Boston and Philadelphia have etched out unique niches for themselves in areas like finance, culture, and advertising. This gives them wealth to address their own problems. Buffalo, Baltimore, and St. Louis don't really have those advantages, and even New York, et al, barely manage to invest in new infrastructure — the kind that will be needed to compete in the 21st century.