The people that have stuck around thus far tend to be really attached to their current location. If you get them to up and move, they might as easily move to another city (maybe where their kids are) then to the new district.
Which might still be worthwhile, or at least worth considering if things are truly as far gone as they appear from those blight maps. If the city is having to maintain water, power, sewer, etc. to an entire neighborhood for a couple of homes, having those people move to a different city and shutting the entire neighborhood down would probably save a bunch of money.
