Also, slotted screws (that they were using) actually cam out before phillips (and aren't self-centering).
It's more likely the self-centering part was more useful to the automated screwdrivers back then.
Sections 7.35 to 7.55 discuss this here:
https://pdfpiw.uspto.gov/.piw?PageNum=7&docid=02474994&IDKey...
Edit: As a side note, they point out that _all_ screws have throw-out, and the only way to not is to have "zero vertical angle is used on all engaging driving faces or the friction between the driver and the recess walls is greater than the axial component of the driving torque." (Section 7.15 in the link above)
They acknowledge that it's possible, but it's not done in their design intentionally.
The original patent is the JP Thompson patent #19008081 (screw - 1932) and patent #2046840 (screwdriver - i forget when)
https://patents.google.com/patent/US1908081A/en
The designers own statements of requiring "zero vertical angle" to avoid cam-out/throw-out is proof Phillips was designed with it to begin with.
The patent change later only added _more_ cam-out/throw-out, it did not introduce it in 1942.
Also, the 1942 patent represents the modern Phillips (which is what everyone would acknowledge is the problem screw), where the original 1932 patent looks more like a Reed and Prince.