And the women fight too..
I think that the Kurdish Peshmerga in Northern Iraq are also driven by a desire to consolidate more (formerly) Kurdish territory under their control mow, while the getting is good.
It is needed for the eventual assault to retake Mosul, and it does keep ISIS pinned down, so they can’t send reinforcements to Fallujah - so the Government in Baghdad can’t really object.
It makes sense for the Peshmerga (for their desired end state, reclaiming Kurdish areas that were ethnically cleansed by Saddam), and it helps the US and Iraqi government in their fight against ISIS, but it is not the big push into Mosul yet. They are still shaping the battlefield around Mosul ahead of time - pulling the front up closer to the city, so it is shorter and requires less troops to man it. This also allows the artillery to move in closer in support of the future urban warfare.