Why were the armies of the ancient period seemingly bigger than the armies of the medieval period?

by Hermelin1997
gynnis-scholasticus

According to earlier discussions on here, it was due to the greater state capacity and organisation of ancient empires compared to mediaeval kingdoms. This is written about by u/dandan_noodles in this thread and by u/Flavivs_Aetivs over here. Just a few days ago this was asked here, which spawned a brief discussion between u/nusensei, u/Flavivs_Aetivs and others. Further answers are very appreciated, should any expert find this thread!