I was just wondering if someone did this as a slight to Sulla in the same manner that crosses were carved into the foreheads of Roman busts.!
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On very many statues from antiquity exserted parts are broken, in most cases hands, but noses are also very often. The purely mechanical reasons are evident. There are no reasons to conclude that this statue was defaced.
Here is one example of the many:
They say this is Cleopatra VII. I do not think anyone hated her so much as to break the nose on her statue. Here are other examples
Of course I cannot prove that in each case the statue was not intentionally defaced, but broken noses, hands, legs are very common.
My favorite ex-seminarian says that he was taught that early Christians were supposed to destroy the power of idols (note the assumption that they had power) by breaking off the nose, genitals, or hands, or any larger destruction. At a certain stage, any statue might be an idol to them.
It may be lack of good excavation that many statues were dug up without a good search for the small bits. His nose might have broken off from the weight of earth on it, and been lying right there, but no one looked for it.