There's tonnes of stuff on those three, but I have never even so much as seen a book dedicated to Persian society or culture. It's like a total blank comes up unless it's related to the Greco Persian war. I have a rough idea of what Rome, Greece, and Egypt were like because of the amount of art and books I find on them, but I know nothing about Persia. Also there are tonnes of stuff on Greek and Greek philosophers and historians, but I don't know anything about Persian ones. Is there any source dedicated to Persian history?
Part of this is simply what we find in popular literature. Because the classical past is very prominent in western memory and is a "prestige" topic it is easier to sell and publish books on the topic; in addition there are simply more people out there with the background needed to write on Greece and Rome. Egypt is less prominent in the "Western Past"(a terrible term but we'll use it) but its monumental architecture and spectacular funerary practices have given the subject a considerable public appeal as well. Having said that, there are a considerable number of very fine books on Persian history before the Islamic conquests. Weishofer's Ancient Persia is a commonly recommended general overview of Persian History from the Achaemenid Empire to the Islamic conquests. For further reading on the Achaemenid Empire in particular, Briant's From Cyrus to Alexander remains so far as I know the standard treatment of the subject, with a extensive bibliography on more detailed topics in the field.
I don't have sources for this answer, so feel free to delete, but here are some general possibilities:
Linguistical access. Roman texts were written in Latin, a lingua franca in Europe for a longtime. Scholars would have been familiar with Latin and this helped some of the revivals of interest in the Romans that occurred during various periods of European history. I am speculating, but I am guessing a European monk/scholar would be more likely to be able to read a Latin text than one written in a Persian script.
Another linguistical point- Greek. Many early New Testament accounts were written in Greek. A familiarity with the language was important to many European scholars in a way that is not the same with any Persian script.
Cultural continuity- Many western cultures have seen themselves as extensions of the Romans or Greeks. In the United States, the Founding Fathers were very interested in the classics. This is reflected in the Neoclassical architecture of the time(See Monticello or the Capital) and even the United State's motto was in Latin originally. The sense of being connected to the Romans or Greeks I think has generated more interest and scholarly work in the west than the Persians.
I agree there is a lack of extensive material on pre Islamic Iran in Western bookstores in the United States, but I'm sure there are much more extensive books on the subject in developed Middle Eastern countries. All you need to do is learn how to read Arabic! As a good general start,I would look up "Achaemenid Empire", "Parthian Empire", etc on Wikipedia,then scroll to the bottom and look at the references. Order those books. Then flip to the bibliography and see what of THOSE books might contain subjects you are interested in...wash, rinse, repeate... Also you could find a local university that has a good history department and look at their Doctoral Thesis collection (or ask a professor for recommendations)