To a Late Modern person like myself, I find it really difficult to wrap my head around what ancient people were thinking when they wrote histories. Why were they so unconcerned with accounting for and remembering events in the way that they actually happened? What was their actual goal in writing histories?
Were they not scared that they would lose memories, or be misled in the future due to inaccurate and biased information about the past?
From a European perspective, the problem is that you're assuming the concerns of modern history (i.e. from the late 18th century onwards) and the concerns of 'ancient people' in writing their works are the same. Although I would say that this really doesn't take into account the impact of post-structuralism and post-modernism which importantly deconstruct this - every work is an account of what the author thinks happened, and can never truly be what 'actually' happened.
They weren't - our concerns with ideas of objectivity and truth and things as they 'might have actually happened' were not theirs. It's problematic to apply our own standards to these works - it's presentism and really doesn't actually help you understand them at all.
To take the example of medieval histories - to critique them as inaccurate accounts of the world and the past misses the point of what they were actually trying to do. The idea for the northern French of the Trojan origin story of the Franks is important not because of its truth (or lack of it), but in what it tells us about how the northern French saw themselves in the world, and how they understood the past.