Interesting story and I'm glad that it ended well but it has almost nothing to do with patriarchy whatsoever. Patriarchy is a social system. What you described was the actions of two individuals that had pretty much nothing to do with that. Both you and the man who assisted you assessed that the panhandler was mentally ill, and wasn't harassing you because he thought that as a woman, you owed him something. The man who stepped in happened to be bigger and stronger and you've noted that the guy listened to him because of that. While it's possible he listened to him because he was another man, there is really no evidence of that in this story. Not all men are bigger and stronger than all women. This guy just happened to be bigger and stronger than the panhandler. You've made a bunch of leaps of logic in order to make a point you wished to make, even though the facts of the story don't actually add up to that point.

Equality doesn't mean we are all clones of each other. Different people have different characteristics, some of which might be more useful in certain situations and less in others. Yes, having a bigger, stronger man step in to assist no doubt made the difference in the guy continuing to harass you, but you also have no proof that the same wouldn't have happened if a short, slight man (or any other bystander of any gender or physical description) had shown up to support you. Safety in numbers is a thing too.

And what about your long-held and loudly touted stance that women should just take care of their own problems as relates to problematic men? Where does this fit into this scenario? Honestely, I'm just shaking my head at this whole thing.