Or anyone for that nature.
When she is first speaking with Jaquen about it, he tells her that if she learns, she can cross all the other names off her list, like Cersei, Payne, etc. So she would be learning to become a killer so she can get revenge on all those who have done wrong by her.
But then when becoming one you cant go kill who you want, just who you are hired to kill, so what is the point? Also the method in which you forget everything about yourself and forget past life 100%. Yes with needle and in TWOW we see what happens when she sees a familiar face.
But the basis of it in general where you have to pretty much forget everything about who you really were and the rule of only killing what is contracted of you to do, what is the point of going through all that to become one? If you cant just go and kill those who you want revenge on, the ones that are driving you to wanting to becoming a silent killer in the first place?