If you built a home out of bricks in New Orleans it will sink. Same (and even worse) for Florida. You can mitigate that somewhat but it's extremely expensive and bad for the environment/water table/aquifer.

For reference, to make a non-sinking, heavy building in Florida you have to drill down into the limestone layer which is usually 100+ feet below the surface. Then you have to create very strong concrete caissons to hold the building up, standing on that limestone layer. It's very similar to if you were to build a structure out into the ocean (LOL).