Well, in general, it's well documented that women don't care all that much about appearance - as long as the guy is clean, dressed in a way that works for him, and has a decent haircut. How a man makes a woman feel is way, way, way more important than what he looks like. This is kind of one of those "everybody knows this except the men who don't want to accept it because then it means there is something else wrong with them" kinds of things.

“Good looks are less important to women — men who score between 5–9 on ‘attractiveness’ actually receive more messages than men who score 10/10,” finds an Oxford University analysis of 150,000 dating profiles. “Both sexes have become less concerned with the income or education level of a potential partner.”

Approaching men can be a safety issue, and there are plenty of ways and instances that women do approach men they are interested in. It's just that women are much, much more likely to want to get to know something about a man before they determine his attractiveness so just seeing him is often not enough to gauge interest.

Once again, expecting that women should handle dating and evaluate potential partners in the exact same way that men do is a large part of the problem.