I would not mind at all if a woman pursued me. I would be flattered and not think any less or differently of her for doing that. Also, it might be a good empathy-building experience for her to better understand how it is for men having to do the pursuing in real life or on dating sites. Might get her to not be as demanding or critical about how a guy might be awkward, nervous, or underconfident, etc. It's very easy to be critical of someone's performance of talking to the opposite sex when you are never doing the pursuing. It's more important to listen to your gut and focus on where the other person's heart is.

Not surprisingly tho, almost the only times that a woman has approached me on a paid dating site with the first move, it has been women who were not attractive looking to me at all, with one exception. I am guessing they made the first move because they were not getting much, if any, interest from other men. The one exception was a woman who had almost nothing in common with me,and hadn't even looked at my profile before sending me a flirt, but was attractive looking to me. I thanked her for her interest and said I was not interested. If I were like most men, I suppose I probably have met her in person, hooked up with her as soon as possible, and then dumped her. Not my style.