That doesn't follow - presumably the desirable men are also getting what they want, less desirable but more devoted women. After all, the idea of the linked article is that a woman who does marry a desirable man would be likely to get a less desirable mate if she were to compete directly with other women.
I'm assuming that early bidding isn't what's working for the less desirable women. It's a self evaluation that they can't compete directly, so they don't. Instead, they concentrate their resources on one mostly-desirable man. Bidding early is one part of the equation, but bidding more is another, probably more important part. If the article is supposed to reflect real life, the timing isn't likely to yield a real advantage, since society discourages women from getting married until relatively late anyway.