There are many algorithms dedicated to building simplification. You may have a look at this website for an overview. See also this question. You could use:
- Building outline simplification: It consist in recursively deleting too short edges of the outline and lengthening the neighbor edges. Example:
- Smallest surrounding rectangle algorithm: It consist in replacing the building geometry by the smallest surrounding rectangle. This rectangle can also be scaled to the building initial area. Example:
- Squaring algorithm: It consists in applying a light rotation to edges to make the corners perfectly squared. Example:
These transformations may be enough for your need. It can be interesting to combine them.
I am almost 100% sure none of these algorithms are implemented in PostGIS. Some are implemented in the Opencarto java library I am developing. Let me know if you want to test it!