This is where those airborne attack helicopters and drones come in. Counterbattery artillery fire is too inaccurate for use in densely populated civilian areas for the reasons you mention in your post. But an operator-controlled guided missile is precise enough to do the job. However, queuing (knowing where to look) when the rockets are being fired still requires some time and cooperation from the enemy (too many rounds from the same spot) to bring weapons on target.
Problem is that artillery and helicopters have probably left the country due to the draw down of forces under Obama and Trump. (Except in the far west where we were, until today, still fighting ISIS.)
Personally, I think we should honor the Shia-dominated Iraqi government’s coming request that the US leave. When we do, I hope we ARCLIGHT every Iraqi Shia militia location we know of into oblivion so that the punks will be sorry forever that they got so upset about their “hero” general receiving his due.
Definitely obey Iraqi legislature’s demand and leave. But keep a potent presence in the embassy for defensive purposes, i.e., copters with guided missile armaments and night vision, satellite targeting and recon support, etc., to take out these punks with their mortars and rockets. As for Iraq, they’ve had a couple decades of guidance and help. Time to cut the apron strings, and should things go sideways, support the side you like with toys and info, and sit back and munch popcorn.
As for Iran, free Khuzestan. Self-determination for the Ahwazi people. That’s the key to everything.