To build more housing, you have to destroy the old housing. This still displaces people, and likely pushes them into smaller apartments where they would have been in a house
What studies show is that poor people move around a lot, whether there's "gentrification" near them or not, for what I think are pretty obvious reasons, and that they aren't any more likely to leave "gentrifying" neighborhoods than they are neighborhoods that aren't gentrifying.
No, you can let people decide whether they want to move out. Many of them would elect to then sell their houses to developers who would build apartments. Many would choose on their own to add units to their own property. If some people don't like living next to apartments, then they are out of luck though. I don't know if we should expect people to have that kind of say over what their neighbors do with their property.
