What a bunch of nonsense. According to all your links significant parts of KSA were part of all those non-important empires. Besides KSA is just one Arab country. Only the Achaemenid was important besides Arabs made many bigger empires. 3 of the 11 largest in world history. All that matters is that you have become culturally, religiously and linguistically enslaved just as before Islam where you copied the ancient Semitic people in the ME in terms of how to rule an empire, by adopting language (Aramaic became the state language), script (you had no script before you adopted the Phoenician based alphabet, made Babylon the capital and all your symbols that are total ripoffs. No, the Elamites had nothing to do with Persians. In short you got civilized by all those people. The only reason you got relevant was due to civil wars in the ME among various Semitic kingdoms and empires.
As I have provided long ago then just 3 Arab countries have won more gold medals than Iran which only wins gold medals in wrestling and weightlifting that are very small sports and that nobody in the Arab world is interested in. Just as the Olympics which never got much publicity nor is there a tradition of that.
Football is all that matters in the ME and here KSA alone has a better football record be it the national team or club teams.
In any case Iranians are still smaller than Saudi Arabians (and Arabs) on average and in terms of fighting skills we know who has the record of being invaded in the ME region by practically everybody around. No, Iran is not fertile but most of it is wastelands.
It's already been proved long ago that most of the Iranians are indigenous let alone the Indians that are 95% native.
The fertile crescent lied in what is now the Levant and Arab/ancient Semitic areas for a reason.