As a man, I will say the very nature of this "solution" is paradoxical. (TL;DR at the end)
As I'm sure you know, some women do hit on men, when they feel safe. For example when they're out with their girlfriends I've seen women turn into absolute horndogs, doing cat-calling, questionably appropriate touching, even in some cases full-on sexual harassment, the whole 9 yards.
Your statement begs the (fair) question: why don't women feel safe openly flirting like that all the time?
In general (i.e. when they're alone), women tend to be afraid to hit on men for the same reason as in this comic, it's just a little harder to grasp/explain.
Let me try: If a woman, alone, sees an attractive man, alone, and decides to "roll the dice" and hit on the man by herself, what are the possible outcomes?
he could be nice, flirt back, and she'll end up liking him and they'll go on a date
he could be nice, flirt back but she might still decide she's not interested and try to say goodbye
(less likely, but still happens) he could give off weird/creepy vibes, and when she tries to walk away, he could try to hurt her or take advantage of her
What you have to understand is that for the woman, Outcome #2 is almost equally scary as Outcome #3. Because women know that regardless of whether they're a creep or the nicest guy ever, a lot of men don't handle rejection well.
I'm not saying you would do this, but ask yourself this: how would most men react if a woman comes up to flirt with them & she changes her mind half way through the conversation & decides to leave? Will most men be okay with it and move on? Or will they take it personally in some way and feel mistreated or get upset with the woman for "leading them on for no reason"?
I have to say, as a man who has interacted with lots of men from lots of cultures, most men, including myself at times, do not handle rejection in a healthy way (even though I've never lashed out at a woman for rejecting me, I've put women in uncomfortable situations out of the fear of rejection).
That is what more men, I feel, need to recognize in themselves, in order for any of this to get better. It's not about normalizing women flirting with men. It's about normalizing men responding to rejection with grace and humility. The attitude of "ah well, better luck next time!" would be so much healthier than the immediate victim mentality most men assume, which is "what did I do to deserve that rejection?". And that is why women have such a hard time feeling safe doing any of that stuff.
TL;DR in order to normalize women flirting with men, women need to feel safe doing so, which will only happen if men can normalize handling rejection in healthy ways.