While not minimizing the dearth of EEs coming out of schools. If we're talking wafer fabs, we're primarily NOT talking EEs. We're talking Chemical Engineers, semiconductor process engineers, physicists and chemists.
Way back when (1980) when I was to graduate with a BS in Photographic Science from RIT (chemistry of light sensitive materials and design of optical systems) I'd sign up for interviews for any company looking for EEs for fab engineering. Inevitably I'd walk in and they'd say "why are you here? We're looking for EEs for our fabs!". After I explained what I brought to the table by way of lithography, image processing, actual process control statistics, etc, I'd get invited out for interview at the fab. Had 6 job offers inside semi industry b4 I graduated.
If they are only looking for EEs they are short sighted.