The proposed corner-shape property (#6521, #6980) means that box corners are not always rounded. This will require that https://drafts.csswg.org/css-backgrounds-3/#corner-shaping is updated other describe how to handle non-round corner shapes.

In addition, shape-outside references the <shape-box>, which may also not be a simple rounded rect with non-round corner-shapes. It's not super clear how a scoop corner shape affects the content box, for example.