They were not highly motivated to keep their hands on the place since it would require substantial investment to bring about a return in trade sufficient to overcome the cost of the conquest. If anything, the Mongols thought about Eastern Europe pretty much the way we, today, think of North Korea.
Your supposition that Eastern Europe didn't suffer to the degree found in Arabia presumed some sort of equality of condition.
There was no such equality. You would have much preferred Baghdad as a hometown even after the Mongol conquest.
The Mongols made normal trade arrangements with the portions of the West that could provide them with furs and dried fish, or which had already had a longstanding relationship with Mongol interests. These places include Hungary, Estonia and Finland (all of which ended up adopting an Uralic-Altaic language as their own).