Remember, it all adds up to normality. Thus we should not be surprised that the conclusion of evo-psych agree with the traditional ideas.

Not if the "traditional ideas" don't necessarily reflect how things have been done for much of human history. Some of the gender norms people support with such arguments are genuine human universals, many others are not.

When people claim that they're final argument tends to be a lot less convincing and involve a lot more mental gymnastics than the original.

I've known people to make evo-psych arguments justifying a sexual status quo which were implausible or even refuted by known anthropology. I think you're assuming a higher baseline level of credibility among people who ascribe to your own position than is actually the case.