I don't think there is such a time. As long as writing has existed it has privileged the viewpoints of those who could write, which was a very small percentage of the population for most of history. But if we want to know what life was like 1500 years ago, we probably want to know about what everyone's lives were like, not just the literate. That availability bias is always going to be an issue for any time period where not everyone was literate - which is still true today, albeit many fewer people.

That was not the question. The question is when do you stop caring about the bias?

Some people are still outraged about the Bible, even though the writers of it has been dead for thousands of years. So the modern mass produced man and woman probably does not have a cut-off date where they look at something as history instead of examining if it is for or against her current ideology.