Why is it incumbent upon men, but not women, to perform the raml (brisk walking) between the two green markers during the Sa'y, even though it is an emulation of what a woman did?

The "ramal" (brisk walking/jogging) between the two green markers during the Sa'i between Safa and Marwa is a recommended Sunnah for men, not an obligation. As for women, ramal is not legislated for them, out of concern for their modesty and to prevent their exposure. Ramal could potentially lead to the uncovering of parts of a woman's body. Scholars have unanimously agreed that there is no ramal for women around the Kaaba, nor between Safa and Marwa, and they are not required to perform idhtiba' (uncovering the right shoulder).