Politically, it's a hot potato. Losing immunity in Iraq means other host countries will demand the same conditions, which becomes a huge political liability for Obama. Then there's the issue of GI's getting arrested and tried on host country soil. That has the potential to generate very ugly headlines for Obama, from a political standpoint. To the extent that Obama wants to be re-elected, he has to insist on immunity, whether or not he personally believes GI's should be immune from host country laws.
I bet if Bush was still in office, we would have gotten the soldier immunity.
We should NOT have troops stationed in all these places anyway.
Troops in Western Europe and Korea, and scattered about the globe for logistical support (Diego Garcia, Guam, etc.) is fine. The rest need to come home.
All these “Poke-a-goat-a-stans” can go rot.