“we can know what influenced chazal, because there are many historians running around with thousands of artifacts, and lots of data from different periods/areas that chazal lived in.”
I would need to see a specific argument to comment in detail. Maybe the have found a way around the logical problems I outlined above.
I will say however that I have read various such arguments in the past and frankly they would not hold water in a court of law (without the Daubert rules). Historians and archeologists are not great on causation v. correlation, they jump to conclusions on weak evidence, fail to consider alternatives that don’t fit their paradigms and, most of all, confuse change in idiom and terminology with change in ideas.
Sof davar: when dealing with the soft sciences don’t just read their conclusions, read the data and the argument and think critically.