But what reasons would they have?
The story goes back to the agreement between Turkey, Iraqi Central Government and KRG about the withdrawal of PKK from Sinjar. At the same time intelligence sources from Turkey revealed that the leadership of PKK is in the Iranian side of the Qandil mountains. Turkey agreed many times with Iran on cooperation against PKK but no fruits came and we saw a real push in Northern Iraq.
The aim of Turkey in Sinjar is to eliminate PKK elements close to the Turkish border and prevent transfer of manpower and supplies by controlling the road between Syria and the PKK camps in Northern Iraq. We know that Turkey will have to allow the US military to operate trough the route but such a situation becomes a problem for IRGC as the route is popular among them to. Iran supported militias in the last 4 months warned many times Turkey and tried to tie the situation together with the operations against US forces stationed in Northern Iraq and especially in Erbil as the KRG authorities are in close relation with the US and Turkish sides and are cooperating on both matters (PKK and IRGC proxy activity). They turned the campaign against the US forces to a campaign against foreign "invaders" in Iraq including against the Turkish intervention. They fired rockets at a Turkish base before thank God without casualties but this time its different. The Turkish military bases in Bashiqah and Duhok have critical importance for Turkey's role in Iraq.
The Iraqi Central Government, KRG and the Turkish trained Nineva militia all failed to provide security for the Turkish border and the Turkish military installations in Iraq. Now it is very likely to see KRG supported push into Sinjar. It is still very early to comment but all the signs shows that Sinjar operation is close and it will most probably be a large push on a couple of phases including a deep push in Avasin/Basyan, Metina and Gara camps including rise of Turkish special operations targeting important traffic on the road between Sinjar and Duhok simultaneously with establishing of temporary military bases and control points in Duhok.