I don't think that's how the typical gentrification process goes though. I think it usually starts with developers increasing surrounding property values which attracts more affluent residents, who demand improvements from the municipality.

The difference I see here is that the developers and new residents are the ones who reap the benefits of the increased property values from gentrification, whereas if the city makes modest improvements before it's current residents are forced out by increasing prices/taxes, then the current residents reap the increased value. Even if they move because they don't want to pay taxes on higher property values, their property is still worth more when they sell it.