It's similar for Icelandic, 1000 year old books can be read if you know the modern language. It probably just has to do with which books are read in elementary school. I imagine that in Iran they read Rumi and Hafez a lot in elementary and high school.
The ease that modern Icelandic speakers have in understanding old texts is not due to Icelandic remaining unchanged all that time. Rather, Icelandic began to experience drastic Danish influence at a certain point, and then Iceland’s cultural elites chose to fight this by standardizing Icelandic on the basis of those old texts. It was a return to sources, not preserving those sources the whole time.