I know that women are exempt from Mitzvos Shehazman Grama, but I was wondering what the Halachik basis is for prohibiting them to fulfill these Mitzos if they CHOOSE to do so. For example, I’m not obligated to go to university, but I am allowed to do so if I want. Why doesn’t the same conclusion apply to women fulfilling, for example, Kriat Torah?
You are right, women are allowed and in many cases encouraged, to perform also Mitzvot they have no obligation to do (e.g. Shofar, Lulav, Succa, etc.) Nonetheless those Mitzvot they are not obligated, they can't perform on behalf of a man that is obligated, or serve as a Shaliach – agent, to fulfill his obligation, that's why a woman can't blow the Shofar for a man on Rash Hashanah or do Kriat Hatorah for men. The reason women are not called up to the Torah in the Shule is based on the notion of Kevod Hatzibur i.e. the accepted respectful public conduct at Shule; as written in Shulchan Aruch OC 282; 3.