Do you expect something exclusively trained on them to be any better?

To a large extent, yes. A model trained on many different accounts of an event is likely going to give a more faithful picture of that event than any one author.

This isn't super relevant to us because very few histories from this era survived, but presumably there was sufficient material in the Library of Alexandria to cover events from multiple angles and "zero out" the different personal/political/religious biases coloring the individual accounts.