The women in my age bracket seem to feel that it is fine for them to be the initiator. I'd say that half of the relationships I've been in have been initiated by me, and half by the other. Moreover, the relationship itself, once initiated, regardless of whom initiated, have tended to be balanced and more or less equitable in terms of what was to happen within them.
I've never been a fan of the characterization of initiation of conversation as a prelude to a potential relationship as "aggression". Someone must step forward and be first, risking the rejection or being termed "creepy" or "pushy", else no relationship could exist. If we are to use the term aggressive when describing the courting process from the standpoint of the one who initiates, and if there are calls form men to be "less aggressive", then where are the scads of women jumping on the opportunity to fill the void that will ostensibly be created? The silence is deafening. This is why your are correct in that it is still a man's issue (although, by this time it should be less so than before). And I don't blame women one bit for not clamoring to step into that role. It's a sucky role to be in.
The fact of the matter is that the initiator bears all of the social and emotional risk. Most people, given a choice to receive/rebuff an advance or to make the advance would choose the former, because it has two advantages.
1. You know immediately that the person likes you.
2. You have the right of acceptance or refusal, therefore the power in the exchange is yours, allowing you to suit yourself without assuming any emotional risk from an unfavorable outcome.
Having experienced both, I can honestly say that I prefer to be approached.