The poor don't need to be displaced unless you artificially restrict growth. It's one thing I appreciate about NYC. There's essentially three types of neighborhoods, organized by price:

1. Cool neighborhoods 2. Convenient neighborhoods 3. Cheap neighborhoods

You can find stupid cheap housing in Queens/Brooklyn/Bronx/Jersey and still be able to take the subway to Manhattan. Why is NYC like this and not SF? Because as the city grows they re-zone neighborhoods (e.g. Downtown Brooklyn and LIC) and expand subway/bus-service further out.