Iran might fancy syria or lebanon , but we have no intention of "conquering" the saudi desert , persia occupied yemen and oman at some point during the course of history , we also supported different arab factions against each other Kuffar vs Mushrakin مشرکین vs christians vs jews , but the saudi desert is simply worthless even today with all it's skyscrapers and state of the art air conditioning systems
Iran itself is one of the driest countries on the planet and has plenty of deserts. In fact the highest temperature recorded in the world was in Iran. Moreover most of the remaining Iran is barren mountains.
You are speaking like Iran was Congo.

Like that would be a good thing.
Most of the ME (cradle of civilization) has an arid like climate and there is nothing wrong with that.
That's why 80% of your population lives in the West of the country near the Arab world (Iraq, Kuwait) and Caucasus. For your information then almost 50% of KSA is mountains and highlands and the agricultural areas in KSA are bigger than some Iranian provinces. Tropical areas are also in abundance in Hijaz and the Southwest where fruits like bananas, pineapples (unknown in Iran) and coffee is grown.
I am sorry but that's not correct. You see you did not really conquer anything in the Arab world. That's why your influence was zero. You did not impose your culture on the locals but on the other hand you adopted our Semitic culture, symbols, language (Aramaic), alphabet etc. All this is well-known and described by historians thoroughly.
The most archaic Persians (probably the only real descendants of Indo-Iranian speaking nomads of Central Asia) are the Lurs who were nomadic and who are still that even today although it is a minority. What did they built? What did they rule? Or create for that matter? Anything that rivals World UNESCO Heritage Sites's (all over 2000 years in age) such as Palmyra, Petra, Mada'in Saleh, Avdat, Hatra etc.? Yes, that's what I thought.
What did your Baloch, Pashtuns and Kurds built (all stateless people) cousins built? Yes, I thought so. Nothing there either.
The Kurds greatest achievement for instance is claiming the history, cities and monuments of the Semitic Assyrians and Chaldeans. That or mass-murdering Armenians, Assyrians, Chaldeans etc.
Is there even 1 monument in your so-called ancestral lands in the steppes of Central Asia? Nothing is the answer.