The problem at the core of gentrification is that when people do end up moving away, those formal and informal networks which helped them all get by are torn into pieces. The problem at the core of uncompromising anti-gentrification is that without growth, the city will stagnate or decay, without any of the money that could make things better (both on an individual level and from the perspective of the city budget.)

Managing this is hard, and will expose a politician to the realities of messy tradeoffs. It's far harder to find the political will to make something work, and much more convenient to shout either "Progress!" or "Oppression!" and make hard problems harder.