Exactly. She obviously didn't marry him for a title or position. As she didn't get one. And she had no reason to believe she ever would, when they wed. Her husband was basically pushed out of succession and she was the unspoken family member. If anything it speaks more to their relationship that she was willing to be the brunt of a lot of horrible press to be with him. How many people accused her of being a gold digger and trapping him?
She could have been a private citizen. Even after they granted her a title. She could have focussed on school and her career. Instead she chose to use it to make a difference. Did she get her charity work because of who she is? Yes. But what royal could say different, married in or born? That doesn't take away from what she has managed to do. Yes Louis has held a lower profile, perhaps why he isn't really known outside of Luxembourg.
So yes she does have a brand to protect. Should all of her good work go down the drain because she is divorcing? How would that benefit anyone? If she was British and not just living in the UK, Tessy, Princess of Nassau would be her title after marriage, would be proper way to address an ex wife.
She is never going to simply be a private citizen. She is a patron of too many charities not to have a public presence. There simply needs to be a way of handling it.
As for her comments on Instagram, she simply answered a lot of backlash questions, and said she was using her title because she still had one. Simple.
Really other then a few throw backs to her husband, I see nothing that says gold digger. Her posts other then about her son, are about her work with numerous charities, usually getting ready or attending them. 
