To cut to the chase, I would say ‘no’. We live in an evolving society and I think we as human being should also evolve to accommodate the changes all around us.
That notwithstanding, there is a reason our society frowns on it. Of course, there is that part where they think women should eternally be passive in all matters but there is also that reason that states that women are precious and worth chasing. Therefore, it should take the deliberate efforts of one who is man enough to win her love. It gives women the honour and value they deserve. A guy doing the ‘work’ gives the guy cause to appreciate her and know his efforts yielded results.
On that note, I am not saying women who approach their men are less valuable or that their men don’t respect them but I am explaining the way society looks at it. Thus, I see no reason why this order should be changed.
However, regarding the initial answer I gave that there is nothing wrong with a girl approaching a man she likes, that is because ideally it shows how confident she is and some men like that. More so, if the guy is being painfully slow about the matter (especially when he is giving hints that he likes her too), should she keep waiting?
Thus, if the girl is sure of the following then she should go ahead:
• That he feels the same way
• That she won’t throw herself at him in the process
• That the guy won’t mind her boldness
• That she is ready for the outcome, whatever it is