"...they believe it will make them better Muslims and part of something bigger than just themselves."
Well, an Islamic caliphate spanning the
UMMA might wall-paper a lot of long-term esteem issues.

The desperation to identify with ANYTHING larger than yourself, particularly as heinous as al-Qaeda, suggests a spiritual emptiness that's difficult to fathom.
It helps to explain the moral ascendancy that al-Qaeda holds over moderate muslims in any debate. That ascendancy seems key in al-Qaeda's more ruthless efforts at suppressing the larger debate. Nobody seems surprised when a muslim moderate is killed. We EXPECT it. So do, worse, muslims.
Thank God for the Age of Reason and rationalist philosophy lest we possibly face the same dilemma.