Using the "wrong" pairing (pozidric screw + Phillips screwdriver or vice versa) results in easier cam-outs in my experience, without alerting the user that they're using the wrong screwdriver.
I personally like Torx and (less so) hex heads.
Wikipedia actually goes into this: https://en.wikipedia.org/wiki/List_of_screw_drives#Phillips
The truth is that it was already pretty hard to mass produce a phillips recess (vs a slotted one) back then.
Once everything transitioned to being stamped, and stamping was easy, phillips became the worst choice for roughly every application.
Edit: I guess the very original patent was edited to _add_ the cam out? I may be wrong on this, but my research showed that the automated screwdrivers on assembly lines did not have good torque controls and therefore were wrecking screws (early 1900s?) and so the cam-out feature was added to help with this problem.
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.
The design was intended to be used in industrial automation settings where you'd very much rather cam out and possibly destroy a single fastener rather than having it destroy your entire part, or jam your line, or possibly blow up your tool.
In what context are you doing industrial automation, but have to worry about overtorquing a fastener? Wouldn't you almost always solve this problem by having a pilot-drilling + tapping step and then using machine screws? In what industry do machines drive self-tapping screws into things?
(I suppose you could dramatically overtorque a machine screw and end up shearing the head off or something; and that this could have been more of a concern before there was any sort of torque limiting built into drivers. But torque-limiting drivers have been around as long as electric drills/screwdrivers have been.)