The increase in value is the result of property prices going up. If you don't own property (like a home), you're not capturing any of that new wealth. Even if you do own property, you're not capturing the increase until you sell your home. If you purchased a home 10 years ago, then the increase of your property value has resulted in a much higher property tax every 3-4 years (whenever the citywide evaluation is done). So your costs have gone up and you're feeling the squeeze. Unless you sell, which most people don't want to do if they have a life here already. Of course, I would guess most families using FRPL are renting and don't own property.

This is another reason why anti-development is counterintuitive but it's specifically for an argument that rich people don't like. If you build more housing, then property values won't be artificially inflated due to a shortage. This means property values... won't go up as much. Of course, if you're already wealthy and you're living within your means you want property to increase in value so you can get a return on your investment (owning property).

One thing you could do is build more of the "missing middle." Condos and multifamily homes. This is property that renters could reasonably afford without necessarily impacting the property value of homes because people who want homes — outside the city, big yard, away from downtown — don't want a condo. But the city doesn't build those units because they change the "character of the neighborhood." They'll say they care about parking and water/drought, but it just so happens it prevents "poor people" (i.e. someone who is not rich) to move into the neighborhood.

Also minor point, Stamford doesn't fit the definition of gentrification. All of the new housing is built on dilapidated land, brownfields, or formerly industrial zoning. With the exception of the Smith which replaced affordable housing, but that's because the owners sold it since they couldn't maintain it anymore. To the extent people are getting "priced out of their neighborhood" it's because of the lack of housing being built, not because old housing is being replaced with expensive housing.