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I'm not sure what your point is. I agree that all of your examples are just further cases where being sloppy about innate vs. learned differences results in bad policy.

The statement "men do worse here because of patriarchal social norms that ultimately end up hurting them" doesn't imply men are responsible for their own misfortune; this seems to misunderstand how society affects its members. In the context of violent crime, an example hypothesis would be that boys are taught by their families, movies, etc. that violence is a valuable part of being male, and because of this social norm, more men end up committing violent crimes. It seems crazy to suggest that a man affected by these cultural norms could have chosen to be brought up in a different environment; I don't know that people are suggesting this when they claim that patriarchal social norms are a problem.

Any research on gender past infancy has a problem in that it's hard to untangle what is "innate" and what is a result of differentiated socialization based on gender.

There's a lot of speculation in this forum about whether this is because of different distributions of IQ, effects of testosterone, etc., but how can we possibly determine if these are true differences or the result of parents, teachers, and other people in society treating young children differently based on their gender?