This question came up for me recently. Note, unlike a Bircas Hanehenin which is optional in the sense that it only comes to be if you want to benefit from something, this is a Bircas Hanehenin that is a Chiyuv, It was about someone in a car accident and his mother (in Israel of all places) begged me to be the Shaliach for Bircas Hagomel. Whilst this appears to be against the Rama, and I have looked a little, a few local Rabonim replied in the negative immediately. I have seen some contrary opinions but alas haven’t studied them in enough detail (yet) to feel confident about them. I have asked Rav Schachter but I’ll need to ring him, as I have a few unanswered questions. Has anyone come across this one. It’s different of course to the husband and wife situation if one uses the argument of אשתו כגופו but I note many women had and have the minhag to say it themselves anyway (either with a minyan in their house — I think it’s a peculiar minyan which has to have two Talmidei Chachomim) or they say it in Shule from the women’s gallery provided it’s not a Chassidic or neo-Litvak Shule of today. Some women, for a Bris, say it at the Bris.