As a practical matter you find that most Ashkenazic adult single women, i.e. high school girls and post high school women, and certainly married women, customarily do not light their own Menorah. You don’t find most frum adult single Ashkenazic women who live with their parents lighting their own Menorah. Most of the divergence is by girls who are children (i.e. pre-bas mitzvah), where some, but not all, Ashkenazic families let them light.
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