It has been established that Marilyn vos Savant is not a genealogist. But I think she has an interesting idea here:
I believe both men and women should keep their premarital surnames throughout life. When they get married and have children, sons would take their father’s surname, and daughters would take their mother’s surname. The benefit to girls and women would be enormous while costing boys and men nothing—except the fun of claiming ownership of the opposite sex! [Link]I don't know anything about "claiming ownership of the opposite sex" (I only rent). But I wouldn't mind trying genealogy in a society where surnames were traditionally, consistently inherited in this way.
If the practice were longstanding, there presumably would be some surnames exclusively male, and others exclusively female. You would have patronyms (Johnson) and matronyms (Janesdaughter). Depending on how their ancestors divided their labor, surnames derived from occupations might differ: Smith and Nurse might be male and female respectively. A woman who bore a son after a one-night stand might have to decide whether to give the boy her own, female surname. "What was your mother's maiden name?" would be a lousy security question for women. One-name studies would split families apart.
Census records could get convoluted if a husband and wife had children by multiple spouses (sons of former husbands, daughters of former wives, each carrying the surname of an absent parent); but convolution can be good if it offers evidence of prior relationships. I don't think the naming convention vos Savant advocates would cause more problems for genealogists, just different ones. At least there would be far fewer women in my database with the last name "______."