A carry letter, for me, is the most plausible way to get my family to take me seriously. A sort of 'yes, I've thought this through. yes, I understand the implications. yes, I've talked to a professional - see?' It's a form of validation if they decide to really get on my case about it.
Otherwise, it's useful if you're in a social situation and get clocked; and in trouble for it. (A simple and slightly poor example would be a gendered bathroom.) Some people have also been able to use them to change the gender markers on their IDs and such.