If the Mitzvah is to hear the sound of the Shofar - not to blow it - then why can’t a man fulfill his obligation by hearing from a lady’s blowing, if the דין שומע כעונה doesn’t apply here?
The Levush 589:1 explains that although in theory any sound should suffice, even from a monkey (or a machine??), however Chazal qualified that it must be a sound that is made by someone who is chayiv in the mitzvah
The Har Tzvi (R’ Tzvi Pesach Frank) is said to of explained that someone who isn’t chayiv is just playing a flute, not blowing shofar for the mitzvah, and such a sound isn’t what the Torah required for the mitzvah.
Based on this, some say a woman shouldn’t even blow for a woman since the second woman will not be hearing a sound of the shofar of mitzvah.