To be less dramatic and more realistic than this headline: there is a small set of economics papers which make use of an inaccurate estimate of populations way in the distant past.

Seriously the fraction of papers in which you see these data used is in my personal experience 0. As a fraction of the total amount of economics research produced annually is probably 10^-6 or smaller. It just isn’t necessary in 99.99999% of papers to make any reference to any national or regional populations 2,000 years ago or more.

Also maybe ask the authors of these papers how seriously they take the estimates OR how much weight they ask the estimates to bear in their papers?? “Not very” and “not much” are the most likely answers.