Why a petal hood for a lens?

The petal hood was designed so that material is removed which would block light at the corners of the frame. But compared to a shorter round hood that is all one length, the petal shape still offers good shielding at the top, bottom and sides. If you have one or can examine one, you will see that from behind, the opening looks rectangular. I suspect that they are mostly (but not strictly) for wide to telephoto zooms. One possible catch (depending on what you are used to) is that you are unlikely to find a cap for the front of the hood. These hoods may look like they would lack strength, but I haven't found that to be the case at all.