If we remove emotive terms such as 'godlike' & replace them with more simple 'unsmiling' 'authoritative', or just 'serious' then we have a place to start.

Portraits of important people used to take days or weeks; the subject sitting for hours at least through the sketch stages, then perhaps returning later so the painter could check some details before presenting the final result to the subject/commissioner.
People having portraits done did not smile, they wanted their image hanging on the wall for 'eternity' impressing all who cast their eye upon it.

With that already solemn view of portraiture, add a technological issue when photography was in its infancy. The first daguerrotype images took 8 hours' exposure. Even though that was reasonably quickly reduced to a mere 15 minutes, you can imagine the difficulty in having someone retain a fixed smile for that time...
They would either look like some mad fixed-stare axe murderer - or move, change expression, try again... the result would be a blur.

So, it was decided that even for technical reasons, it would be better to have the subject maintain a relaxed expression - no smiling. They often had head or neck restraints to assist them in keeping still.
There's even the additional issue that most people's teeth in those days were probably not best on permanent display. Dental hygiene was almost non-existent, even for the rich. Teeth would not be as white & shiny as you'd expect in this day & age... not a good look if you want to look impressive down the annals of time.

That brings you to a series of serious unsmiling lawyers, trying to look authoritative for 15 minutes - the very definition of po-faced.
So really, the reasoning is both cultural & technological.