“Guessing @emilybee 's Albany example is similar…I’d guess Albany isn’t eager to have the capital move to another city and take all the jobs with it, despite the property tax situation.”
The biggest problem is that homeowners property tax is even higher then in the most affluent suburbs which, not coincidentally, also have the best school districts. The public schools in Albany are not good at all - so on top of the higher taxes homeowners pay - add in 13 years of private school. Most state workers do not even live in Albany. We have suburbs with larger population than the city.
City of Albany just got an additional $12.5M from the state in this years budget to help out.