The current Chronicles civs may make you forget about this fact (thanks to the Greek civs having weak cav and very strong infantry) but the truth is that AoE2 is inherently a bad game to represent the period since a lot of of the game is built around heavy cavalry.
Imo one of the most important things is that horses were weaker and smaller, during the classical age and therefore no bloodlines could represent that. I think the Chronicles civs keeping supplies is also good since the early middle ages were marked by an imposibility to supply and feed large armies (in Europe, that is)