That assumes the women don't want sex without marriage, a woman can have sex with a different man every night and that might be the reason they choose to go this route --just like the men do.
Well, OF COURSE a woman can have sex with a different man every night. That's the point: she always could. Men are hardwired (no pun intended) to be ready, willing, and able to engage in sex at every opportunity. The sex drive in men is strong.
While woman are fully capable of enjoying sex (something I enthusiastically encourage), it is NOT the natural primary motivator for their entering into relationships (with rare exceptions). Unscrupulous men who understand women often take advantage of this aspect of female psychology to seduce them, telling lies about loving them, giving false hope of commitment, etc. It's as old as the hills.
In the past, most men had to control their drives because women demanded that sex be confined to marriage, which was to her, and the subsequent children's advantage.
Now, men don't need marriage to have sex, so the ladies are out of luck.