The U. S. Senate wants women to register for the Selective Service just like men do. It makes sense because the only reason the High Court gave for not drafting women was that they were not allowed into combat when the draft was challenged during the Vietnam war. There is another reason not discussed because it is not politically correct.
A draft should be about national survival. We should not compel people into a war unless it is necessary for national survival. While everyone is important, a nation can survive the mass loss of its young men but not of its young women. Women of child bearing age are vital to the continuation of a nation. You can allow multiple spouses for a time to replenish a population, but that would not work if you lose massive numbers of young women. Frankly, we cannot afford to put millions and millions of young women in combat.
Women who are properly trained are great warriors. Still it is likely that in certain combat roles women would have lower rates of survival than men. If you discriminate and put men primarily in dangerous roles and allow women to choose, you will hurt morale of draftees. Either way will hurt the war effort.
In a volunteer military, you do not have the same issues. In a draft, it would be a different world. Drafting women is not good for national survival and we need an honest conversation about it.