Archaeologists study the past through material culture; from artifacts to bones to pollen samples. Historians study written sources. Which is not to say archeologists don't make use of the written sources nor that historians don't pay attention to archaeological results. But the point is it's a historian that'd be more likely to be doing a translation. (Or a historical linguist)

Anyhow, the point of translation is to make the text accessible to a modern reader and read as it would've read to the person reading it at the time it was written. Or at least the translators interpretation of what that is, all translation involves a certain measure of interpretation.

Now if I translate, say, Old Norse into contemporary Old English I'm not doing anything useful for a present day English speaker, for whom Old English is nearly as alien as Old Norse is. But even with a more modern language like 17th century (early modern) English which is mostly understandable to the present-day speaker, it's not really a good idea. You're making it come across as archaic where it didn't read like that to the person writing it.

It'd be difficult to do in practice even if you wanted to. Compared to the number of people able to read Shakespeare, very few can write in the language of his time. When should it be 'thou' and when 'you'? 'Go' vs 'goeth', 'shall' vs 'shalt', 'old' vs 'olde'?

So most of the time it'd just be making life harder for both the reader and translator for no good reason.

That said, because of the status of Shakespeare and the King James Bible, English of the early 1600s specifically has a particular prestige that can be (and is) sometimes used for literary effect. Not so much in modern academic translations but certainly those of more literary character, where (say) if a god is speaking a commandment and a corresponding sense of haughtiness is required. Or because a passage is archaic language in the original and you want to convey that somehow.

To continue that example of Old Norse, if you look at translations from the 19th and early 20th century (which are easy to find since those are the ones out of copyright and free online), they often make choices that are odd, or at least considered outdated. They used archaic language (by the standards of their own era) out of a kind of desire to reflect how old the texts were. They'd sometimes do odd things like try to preserve the Old Norse word order, which is a bit nonsensical since it was a more inflected language with a much freer word order than modern English has. And they would fall for the temptation of using old English terms that were relatives (cognates) of the Old Norse ones, like rendering the Norse "hæita" ('to be called') into "hight", an obscure and archaic term even in the 19th century.

Which brings me to another point: At least in some ways it's trickier to translate between closely related languages than languages that are completely unrelated. Because when you have words that resemble each other in appearance and meaning there's an natural tendency for your mind to go to that word first when considering a translation, whether or not that is actually the best translation. Often these are words that have a common origin but which have undergone different changes in meaning (semantic drift) since then.

For example, the word "stark" in English and the word "stark" in Swedish share a common origin. But in Swedish it means 'strong' (as it formerly did in English) and is mostly used as 'strong' is in English. But you would not describe a muscular person as being 'stark' in English and you would not describe the weather as being 'stark' in Swedish. The more closely related two languages are, the more such pitfalls there are going to be.

Anyway, so as a rule, historians translate into the modern language.