How does Hester Prynne’s sentence of having to wear the scarlet letter on her clothing beneficial to her long-term, even though it stigmatized her and made her the subject of ridicule and scorn initially?

In my opinion, the letter is never beneficial. The meaning behind the letter changes over time, but with or without the letter, Hester was Hester. Over time, people saw her the way she was.... a helpful, caring, talented woman. Purposeful shaming did not achieve what people initially intended, though their ridicule was hurtful. None-the-less, Hester went on and did the best she could for her daughter.... Pearl was her purpose..... letter or no letter.