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Why did the author choose "would have" instead of just would or the past tense in the following example?

"many of his fellow academicians took it for granted that Caligula, Cleopatra and Julius Caesar would have written their letters in French, and Pascal, Newton and Galileo would have written to each other in French, when every child knows that educated men in those days wrote to each other in Latin"

A good question!

Although these instances of 'would have -ed' may appear to be in the conditional mood, they are in fact indicative.

'Would have -ed' here is simply the past tense equivalent of 'will have', indicating a probability or expectation that something had previously occurred, as in

I don't suppose you need dinner, since you'll surely already have eaten before coming here.