But why does anyone believe that officially approved "role models" will do anything to change this? Young women will laugh at this idea, as they do at other manifestations of unwelcome adult authority. Celebrities should do everything they can to avoid being appointed; it will be the kiss of death.
Teenagers will pick their own role models, ignoring what those in authority think, as they have since the inception of a separate "youth culture" in the Fifties. Rebelling is a natural part of growing up. Picking your own heroes is one way of expressing that rebellion, and by ignoring this, the minister's ideas simply become patronising.
They are also unrealistic. Sophisticated advertising agencies spend millions trying to keep up with 14-year-old tastes, and often fail to do so. Why should we think that government is any better at hearing what the young have to say? They have not included in their prospective list Baroness Thatcher, that most powerful woman of recent years; the choice does not therefore seem all that far from a Stalinist "approved list" of the politically acceptable. That is why young women will ignore it. Anyone the Government likes is by definition not likely to be popular with the young.
The Government itself does not seem that committed to creating powerful female role models. Why does Cherie Booth, successful barrister, have to appear with the Prime Minister as Cherie Blair, dutiful wife and mother? Mr Blair's inner cabal appears to be made up mainly of men; a laddish heart often appears to beat at the heart of New Labour.
There is, of course, nothing wrong with having a women's unit in the Cabinet Office, screening policies that affect women. If nothing else, at least ministers will be made aware of the impact of their policies on half the population.
But you wonder whether the unit will achieve that much. This Government has done much to empower women without relying on selective policies. The minimum wage, the working families tax credit, increasing family allowance, flexible hours for nurses, and helping with child-care costs are all real achievements that primarily help women, but have a broader effect and appeal.
If a women's unit at the heart of government speeds such progress, than all the better. There may even be a case for similar scrutiny of measures affecting ethnic minorities, or people with disabilities. But the women's unit - and its ministers - would be better employed working on real measures than on gimmicks designed to associate New Labour with social changes they can neither control nor predict.