Anytime someone mentions that she can't kill because they think she has some 'morality' thing going on, I just roll my eyes. Like, bold of anyone to assume that Eliza actually needs to go on some long emotional journey whenever she kills someone. OKAY sure, she doesn't necessarily always use … lethal force, especially when she is working with the Avengers, it's not her call to make. She doesn't lose sleep over the killing. But if she's working alone ?? Then you better say your prayers, and she just might make it quick.
What makes Eliza such an efficient assassin, training and abilities aside - there is part of her that enjoys the hunt sometimes smiling while her target struggles to fight her.