When I was a child, I have noticed that many PAR38 incandescent, halogen, CFL, and ceramic metal halide reflector lamps often had hexagons in the center of their front faces long before the advent of LED lighting.

Why is it the case that many PAR38 reflector lamps have hexagons on their front faces?

I believe this has to do with trying to attain a more symmetrical beam profile.  One of the first such designs was introduced and patented by Tungsram, which added two linear lenses moulded into the front.  They were positioned parallel to the CC-6 horizontal filament so as to broaden its beam in only one plane.  To improve efficacy by providing less scattering of light that in any case travels from the filament directly through the centre of the lens, they eliminated the miniature lenticules from that area and replaced it with a stippled structure.  See for instance US Patent 4,651,261 of 1985, https://depatisnet.dpma.de/DepatisNet/depatisnet?action=pdf&docid=US000004651261A&xxxfull=1

I suspect the only reason that ended up hexagonally shaped was because that is the natural close-packing structure of the small lenticules over the surface.  If they had tried to make a circular hole, it would not have had such a regular edge profile and would look a bit unprofessional.

An almost identical design then was then applied on German Osram PAR38 lamps.

Around the same time Philips moulded a full hexagon into the front lens of its PAR38 spot beam lamps, with six radial lines from each corner of the polygon.  I have not found a patent for that but suspect it may have been an improvement over the Tungsram/Osram designs.

It would be interesting to study some older PAR38 lamps to see when was the first origin of the hexagonally shaped area at the centre without lenticules - I think that was a much older invention.