What a deterministic answer.
Just because Iran did not have such a population in OTL does not mean it could not acquire one. Just do not have epidemic warfare ravaging the heartland and the population would naturally grow and urbanize.
It's not deterministic, it's geography and climate.
No it does mean that, "only because Greenland did not have such a population in OTL it doesn't mean it can have a million people IATL". The population of Iran had plenty of time to recover since Timur up to the 20th century, it didn't grow super high because the geography and climate doesn't allow it, it's not like China was limited long term by warfare with the Mongol or later famines and Manchus.
Urbanization wouldn't increase the population more than 10-20%, by itself at least.
The Mongols destroyed irrigation and other vital infrastructure across the Middle East that had allowed for large urban populations. In particular the Iranian Plateau was ravaged oven and over again by the self proclaimed Mongol successor states and Turkish Empires. The population never recovered until the early modern period. Iran is big. It is located on the trade routes between India/China and the West. Has the potential to unite/rule all Muslims as the Caliphate. I see no reason that in a timeline without the Mongols it could become one of the most dominant states in the world. A hegemonic, prosperous, and colonizing Superpower.
Yes, exactly, it
did recover in a couple centuries, so why would it grow so large beyond that? Being big doesn't mean anything if you have deserts like Dasht-e Kavir/Lut.
Being located between trade routes didn't make the Tarim Basin or Central Asia any more prone to have big population densities, merely bigger cities and urbanization rates.
You see no reason, I see the fact the terrain has physical limitations and people can change it only so far.
Is exceeding the population of Pre-Black Death Europe difficult? Yes it is. I admit that. But Europe prior to the Black Death was teetering on the edge of overpopulation and famine. There were several famines in the years prior to the outbreak of the plague. The nobility and the church will be unable to do anything, they will blame each other and/or God for the famines. There will be no outlet to the New World here. It is several centuries off. Without the Plague we would still be looking at a "time of troubles" that would be no less catastrophic for Europe. We would just be starting epidemic warfare we saw on the continent during the 1600s/1700s early. If you think that, no they woulden't have the money to pay for that, remember that the worst war during that time period, the 30 Years War, was so bad because all sides ran out of money and the armies turned to looting instead.
Avoiding the Black Death is one of last PODs that could lead to a Europe screw like this. It is important to bring that up.
What a double standard, geography and climate doesn't matter for Iran but "Europe was teetering on the edge of overpopulation", wouldn't your Persia be as well? You are pushing a population in side of Iran 2 to 3 times as big as it was during its golden ages.
Warfare in the 17 to 18th centuries was not caused by population, nor is the 18th century European warfare "epidemic", also interesting the fact you use "determinism" when frankly malthusian minded determinism is a more extreme position than pointing out that geography and climate are still largely uncontrolled by humans.