> Why wouldn't the people who prefer this just take the developer's money, buy another house somewhere that hasn't been rezoned and pocket thousands of dollars?

This one is obvious - they want to live close to where they've lived so far, and they want to stay in their house. Rezoning will inflate the house prices in the vicinity (because of the effect that you're describing of people moving close) so the residents won't feel confident that they can keep affording that area, and won't be pushed out into the countryside.

> Individual flats will be somewhat more affordable than they are now because supply will increase.

This works if the supply will overwhelmingly (in the scale of the entire metro), exceed demand. Here multiple things can happen. One is that demand increases with supply, prices of the apartments go up and match the prices of houses, and prices of houses will grow like you predict. The other one is that people don't want to live in a mixed zone neighborhood, the developer won't make money, so they'll build cheap slum housing instead of normal housing, and the value of the houses in the neighborhood decreases with the new construction. This really depends on the real world situation, and can't be accurately predicted with a supply and demand model.

> Higher density areas allow mass transit to become viable, which reduces car traffic.

People from the burbs don't want to take the bus, so they won't vote for that.

> To begin with, if you convince them then they vote for something else.

Good luck with that, but if you look back in 10 years, we'll be in the same spot.

> Moreover, the status quo is self-destructive. As prices go up, fewer people can afford a home, and then if it's homeowners voting for the status quo, they become a minority and get overruled by the growing number of people who can't afford housing.

This assumes the majority will vote according to their interests. They likely won't. The power to manufacture consent is still with the owning class.