Natasha's arc is also about that to me (and as you said, choice). Going from being forced to constantly adapt to be whomever she needs to be/ what others want her to be, to being "herself" even if she doesn't know who that is. One way to read her sort of inconsistent writing across movies is that she's trying out different version of herself, for herself. To me, her hair represents this. It might be long, short, curly, straight, different shades, but it always red. There is always an integrity to Natasha, but outside of that she's changeable.