Arya is not the a proper child, that’s the point. People ignore how conscious Arya is of her lack of properness and her failure to live up to the traditional standards shoved down her throat. Arya can’t sew, but she offers to make Sansa a new dress anyway. She tries to appease Lady Smallwood & wants to be more traditional just for the sake of pleasing her mother- Arya discovers that properness is a class issue, not a moral one. So long her heart is good, she has no reason to yield her true self