Being able to handle arbitrarily polygons isn't insane complexity, it's actually the minimum viable complexity needed to handle any basic shape a user might wan

Being able to handle arbitrarily polygons isn't insane complexity, it's actually the minimum viable complexity needed to handle any basic shape a user might want to use. Limiting them to a handful of precomputed ones is the kind of limitation only a software developer can live with and love. And once you can handle arbitrary polygons, writing and maintaining special case code has to be justified with evidence that your code is spending enough time on area calculations that it's worth optimizing and maintaining extra lines of code for.