Although she became the first woman staff writer and columnist for Life magazine, she was best known for her participation in the "Point-Counterpoint" debate segments of 60 Minutes in the late 1970s with conservative James J. Kilpatrick.

She fell into writing when she took a summer job as a copy clerk at the New York City newspaper PM, where her mother worked.

[6] In 1962 she wrote an article for Life entitled "They Decide Who Lives, Who Dies: Medical miracle puts moral burden on small committee,"[7] which sparked a national debate on the allocation of scarce kidney dialysis machine resources.

She played down this part of her career, commenting in 1979 that prior to that she "had been a writer, a columnist for Life magazine and for Newsweek -- that was about as high as you could get in column writing.

"[5] Still, the debates Alexander had with Kilpatrick were so prominent in American culture that they were famously satirized on Saturday Night Live, with Jane Curtin taking Alexander's role on the “Weekend Update" segment opposite Dan Aykroyd's version of Kilpatrick, arguing two sides of a topic in the news.

Her book Nutcracker, about Frances Schreuder, the convicted socialite who persuaded her son to kill her millionaire father, was made into a 1987 TV miniseries.