Not sure how open you are challenging your perspective. Because in some ways, yes lifting weights does work for a certain subset of women.

But if you take the dominance angle, dancing works better here. Because it shows dexterty, moving along with other people .. and self confidence in a social setting. Knowing how to dance through life. Not awkwardly stand aside. And lifting weights (on its own) is just a indicator of muscle mass, not muscles in combination with brain, which is evolutionary much better. Otherwise we all would have evolved as big bulls.