I agree. I think the problem very much starts with the sculptures themselves. It seems rather likely that the sculptors would have had an incentive to "improve" some of the not so attractive features of those very powerful men.
A realistic ML model could theoretically compensate for that by reintroducing a bit of variability based on the variability we see in today's population of that region.
On the attractiveness point, the author mentions that in the case there were multiple visual sources, the one which would likely be considered less attractive was chosen. (Under the assumption that it was probably more accurate since as you stated, there was likely incentive for flattery.)
It certainly hasn't remained exactly the same, but there could be quite a bit of similarity left:
It is generally agreed that the invasions that followed for centuries after the fall of the Roman Empire did not significantly alter the local gene pool, because of the relatively small number of Germanics, or other migrants, compared to the large population of what constituted Roman Italy.
In 2008, Dutch geneticists determined that Italy is one of the last two remaining genetic islands in Europe, the other being Finland. This is due in part to the presence of the Alpine mountain chain which, over the centuries, has prevented large migration flows aimed at colonizing the Italian lands[1]
The migrants comprised war bands or tribes of 10,000 to 20,000 people,[5] but in the course of 100 years they numbered not more than 750,000 in total,[citation needed] compared to an average 40 million population of the Roman Empire at that time.[2]
A realistic ML model could theoretically compensate for that by reintroducing a bit of variability based on the variability we see in today's population of that region.