As pointed out in said prior application, one of the principal objects of the invention is the provision of a recess in the head of a screw which is particularly adapted for firm engagement with a correspondingly shaped driving tool or screw driver, and in such a way that there will be no tendency of the driver to cam out of the recess when united in operative engagement with each other.
Another object of the present Invention is to provide a screw head with a tool-receiving recess’ which may be produced by a simple punching operation and at the same time preserve all of the desirable virtues of the screw head and the recess therein, and which results in certain additional advantages, namely, the screw head is left stronger near the outer edge than heretofore possible; the recess firmly and adcurately receives the driver and causes the driver to centralize it self with respect to the screw head.
The head was designed to be cheap to manufacture by cold-forming the metal.
To add to the other explanations - Philips was designed to cam out to prevent over-torque during assembly work.
That’s just a myth. From the 1935 patent US2046839A by Phillips Screws Co.:
The head was designed to be cheap to manufacture by cold-forming the metal.