Compulsion cannot be used on people easily. It provides a powerful, irresistible desire to do as you have been commanded, but overall it is more destructive than helpful to the person who wove it originally. The one exception would be someone who knows how to wield it skillfully and extremely subtely, and the only person I know with that extreme aptitude is Graendal. She can compel someone to the point that they can actually act normally to the casual eye.

Aran'gar seems like a relatively unskilled channeler and would not be able to pull off Compulsion on Egwene without causing significant destruction to her own plans. Masema is an example of a compelled person - he's feral in his desire to perform a command and it shows. We've had Egwene's PoV and there are no indications of Compulsion or her struggle to battle an abberant thought. When Moghedien used Compulsion on Nynaeve, we could see Nynaeve's internal struggle.