Of course, Iraq and Persia saw extensive destruction of their infrastructure.
Which was not due to the Mongol conquest. The invasion of the Ilkhan only pushed a dead Iraq over the edge and Iran was hurt more by Timur than by the Ilkhans or Temujin; both of which did extensive damage to Central Asia, such as Urgench and Samarqand. Both Iran and Central Asia recovered from the Mongols and Timur and had extraordinary states in the 1500s, while Iraq continued to deteriorate.
Thus, I see another reason for Iraq's decline:
1. The Zanj rebellion. All states and areas require two things to keep a large metropolis (city) going. Those two things are an abundance of farmland and an army to defend it so that merchants feel safe to do business.
Within Iraq, Baghdad was dépendant on the large plantations and agricultural property in the extreme south of Iraq in what is called the Batihah Sawad, which extends from the far south of the Baghdad metro down to Kuwait where the desert begins (or better yet, began). This area was the ancient land of Sumer and Babylonia, the land famous for the oldest and greatest of early civilizations and what Muslim chroniclers call the Garden of Eden and the birthplace of Mankind. By the mid Abbasid of period, this area was populated by thousands of slaves from all parts of the Islamic world, but most definitively, Africa. These slaves worked on the vast lands of the south of Iraq and supported the massive growth of Iraq which was built from the transfer of the old city of Cteshipon-Seleucias which was demolished earlier to build the so called round city of Baghdad.
All of this farmland unfortunately became the site of one of the most vicious wars in Islamic history, lasting around 30 years, far longer than the Mongol conquests. This war further was centered around the Abbasid army chasing Zanj forces who burned the land over and over again and sent nobles and planters fleeing away from Iraq. The end result of the war was thousands of casualties on both sides, the incalculable destruction of the Sawad agricultural land, the burning of the most important cities to the defense of Baghdad and the utter terror employed by the rebels on Muslim peoples who never experienced war at such a level.
This area of the Sawad has yet to recover from this war and infact got and gets worse every year. The desert began to eat away at every oasis on the fringes and farmland that the Zanj burned over and over for 30 years. Nothing, I repeat nothing compares to this level of destruction that the Mongols did in terms of Iraq.
2. The Khawarij revolt.
The Khawarij revolt of northern Iraq. A climax of extreme persecution of Shi'i and various other Muslims led to a vicious war in the north of Iraq that would last nearly 40 years of constant raiding and ethnic cleansing. Within years, Arabs were slaughtered throughout the north of Iraq as Khawarij armies filled with Kurds attacked unprotected villages all over. Christians whom the Abbasid relied on for tax where massacred as the Khawarij destroyed everything they came in touch with, Christians who lacked an army to defend them or weapons to resist. These rebels ran simultaneous to the utter decline of the Abbasid state as in the fields of Anatolia, Umar al-Aqta a famed muhjahid was struck down at Poson in battle with Byzantium.
Khawarij in the end wiped out entire areas and sent people fleeing all across the land. Christians especially fled with reckless abandon to the north in Armenia to risk becoming slaves; better that then to be under the Khawarij raiders. As well, thousands of Christians fled into Edessa to be protected by the Armenian warriors who opposed the Khawarij and Muslim alike. This war disintegrated one of the most important provinces in all of Islam.
3. Invasions.
The Abbasid throne coming to grips with the break down of society in Iraq was beset further by secession on all sides. The rise of the Saffarids and Tulunids caused strife and fear and the loss of massive areas of troop recruitment. As well, the Saffarids marched onward toward Baghdad. These wars were the catalyst for the last great sign of Abbasid life, but also the death of an empire. As the Abbasids defeated all opponents and nullified them, they too weak, fell to the next opponent and would be ruled by the Buyyids which commenced a second war in the Sawad against the Qarmatians who destroyed Makkah and against the Grand state of Batihah a state of ruthless pirates.
To add even worse injury, the Saljuq period saw the destruction of traditional Iraqi farming methods and the handover of land to nomadic elites. Saljuq authority did assist however in quelling the Fatimid and Byzantine threats which creeped on the west and ended some of the Da'i states formed by Shi'i supporters.
So no, Iraq's situation is not the fault of the Mongols. But simply, a combination of events from the Neo-Assyrian period all culminating in the 830s-940s Iraq then ending in the Mongol conquest of Iraq in the 1250s and subsequent rule by Mongol rulers such as the Jalayarids and Timurids.
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