So, do you mean that girls should just stay as a comel little kitty and wait for someone to approach them? And that their feelings should be hidden and be useless?

Approaching someone you have feeling for is not "DESPERATE", at least not always the case. More modern woman particularly the younger generation are equipted with education at the university level, grow up in/with a more open-minded family/parents, surrounded by easy access resources and more. 

We learn that, if you want something, you have to go after it. Waiting = time-wasting, also, we learn to express our feeling more. All-in-all, female has always been more expressive than male.

If you think that a woman approach you is due to desperation, you must feel happy that you could now rest your right hands, as one finally come forward to stroke your long buried ego.