I’ve sort of read that during those times people wouldn’t dare to destroy ancient statues, because people thought they were possessed. Also during iconoclasm, the statue of Irene I mentioned was made by constantine VI, member of the isaurian dynasty and an iconoclast symphatiser. Since his father and grandfather was an iconoclast.

I suspect it has more to do with the 4th crusade and the post 4th crusade empire, as they had barely any money to maintain anything monumental and everything around them was crumbling.