Except that it does work with an Opteka iISO flash on an A7II with the LA-EA4. So, it's not impossible... just weird. There are plenty of other things wrong with that Opteka flash, but they - possibly by accident - got the AF assist to work.
Note that it does not work with this same combination on an A7. Another combination I tried is the Minolta 3600HS(D) on both the A7 and A7II with LA-EA4. No assist with either of these combinations.
I don't know why Sony messed this up, and I really don't know why they refuse to fix it, other than maybe more of trying to push people away from A mount lenses.
Its not really about A-mount lenses, its about the MILC sensor. My believe is that it was intentional. The traditional AF assist beams are IR-based wavelengths and MILC sensors have an IR filter. The belief is that since the AF is performed at the sensor, the AF assist beam would never be seen by the AF system due to the filter. It is likely they disabled the AF assist lamp signal from the camera intentionally to avoid support requests saying "Why doesn't my flash's AF beam seem to actually improve AF speed on my mirrorless body?????". So the flash is likely not even seeing a request for AF assist.
Your example of the Opteka flash with LA-EA4 works is because that adapter has a complete SLT PDAF system built into it (bypassing the MILC on sensor AF system), so a traditional IR assist beam would be seen by the adapter's AF system. I am not sure why various combinations of this adapter/body/flash are not consistent.
They couldn't have firmware updated existing flashes to use a different wavelength of light for the AF assist beams, so there isn't a way they could have worked. (at least the pure IR ones).
So then in later flashes, they added an LED-based AF assist lamp which would be seen by the sensor and likely altered the triggering spec to have a traditional AF assist firing mode and a new AF assist mode for the LED lamp. As someone else mentioned already, it was only after this change that Godox X1T-S firmware update allowed the AF beam to trigger. The Godox likely looks for the new signal type and fires its non-IR visible AF assist beam, etc.
Presumably, other flash/trigger manufacturers using non-IR AF assist beams could take advantage of this new mode/trigger and update their firmware accordingly.