The way this was dealt with historically, for better or for worse, was to put the cheap housing under the flight path. The proles were left to deal with the noise. The Harlem neighborhood of Kansas City North is a good example of this. It sits next to MKC and has a flophouse motel, a car repair shop, and little else.

When aircraft got significantly faster, heavier, and larger with the advent of jet airliners, it became less of a noise issue and more of a safety issue. You can tell people to put up with noise, you can't tell them to put up with a huge airplane falling out of the sky onto their homes.