The curved walls also help reduce the stress on the socket walls, and so make the socket itself stronger too.
There are several different names given to sockets that apply the torque to flats of a fastener, by different manufacturers.
Some common names used by manufacturers for this feature are: ‘Hip-Grip design’, ‘Anti-slip drive’, ‘OGV’, ‘Opti-Torque’, ‘OZAT’ and ‘AF’.