Babylon of the Old Testament and “Mystery Babylon” of the New Testament are two distinctly different things, so confusing them is a big mistake. Mystery Babylon is pretty clearly identified in Revelation, and it isn’t in Iraq.
I agree with you that Mystery Babylon is a religious system.
Rev 11:8 (KJV) - “And their dead bodies shall lie in the street of the great city, which spiritually is called Sodom and Egypt, where also our Lord was crucified.”
Where was the Lord crucified? Jerusalem.
What cities have 7 hills? Rio, Rome, and... Jerusalem. Every Jewish school child learns the names of the 7 hills of Jerusalem.
Jerusalem is also called Babylon, a prostitute, faithless wife, dead vine, etc.
A prostitute or faithless wife is a false religion in the OT if not a ref. to a person like Rahab. Babylon is where the false religions began, then spread, and we have the false Babylonian Talmud and Kabbalah to this day.