Martha Burk and Eleanor Smeal make the case for it in the WaPo today:
Why is the amendment needed? Twenty-three countries — including Sri Lanka and Moldova — have smaller gender gaps in education, politics and health than the United States, according to the World Economic Forum. We are 68th in the world in women’s participation in national legislatures. On average, a woman working full time and year-round still makes only 77 cents to a man’s dollar. Women hold 98 percent of the low-paying “women’s” jobs and fewer than 15 percent of the board seats at major corporations. Because their private pensions — if they have them at all — are lower and because Social Security puts working women at a disadvantage and grants no credit for years spent at home caring for children or aging parents, three-quarters of the elderly in poverty are women. And in every state except Montana, women still pay higher rates than similarly situated men for almost all kinds of insurance. All that could change if we put equal rights for women in our Constitution.
How would amending the Constitution lead to more women in Congress, a smaller gender gap, etc.?
Later on, Burk and Smeal identify policies that an amendment could plausibly affect. But the public doesn’t overwhelmingly support the policies in question: notably, banning single-sex public education and putting women in combat. The point of the amendment would seem to be to use a vague aspiration to get through the courts what feminists can’t get through elections.