woof wall of text!! i'm grateful you put in this much effort :). let's see if i can cogently put all my thoughts together here.
I think you some good points about patriarchy theory reinforcing sexism. I think it's a good way to introduce the issue of power imbalances by holding a mirror to the issues of agency/vulnerability but it stops short of being completely successful because of its sort of entry level nature. The absence of intersectionality in feminist theory severely limits the narratives and potential for change and reform even amongst women. I think kyriarchy is a better, more enveloping sense of theory that accounts for the multiple, intersectional sources of power beyond simply gender.
However, I disagree with your interpretations of institutional gender oppression. Just because a standard of treatment isn't codified in law doesn't mean it isn't structural. There are many sexist social practices that continue to be perpetuated and continue to hold women (and, by proxy, men) back. It does boil down to the same assumptions of agency and vulnerability but that doesn't make them any less real.
That said, I think it's not possible to do away with entry level theories like patriarchy theory because there will always be a segment of the population that can't or won't understand the massive overlapping webs of institutional oppression. Theory is inaccessible to many and explaining it in simple terms is often a better way to begin a conversation with people outside of academia, which I would argue is the larger portion of people participating in a society.