I think you are missing a larger point. The conflict in the Middle East has evolved into a widening Shiite/Sunni rift. A pipeline from Iran to Syria via Iraq would represent a pipeline beyond the control of Sunni energy powers, and to the Shia that matter more than raw economics. Assad is a Shia Alawite and that minority rules Syria.
All of the discussion has been a pipeline from Qatar, not Iran.
I don’t think we will see a pipeline from Iran going through Iraq in our lifetime.