PUA coaches endorse the patriarchal view of women's weaknesses and vulnerabilities, and they teach men how to exploit these for sex by adopting the strategies of old-school cads.

I think most pickup coaches would object to this point of view, and it might make some of them quite unhappy. PUAs teach strategies that they believe will increase your attractiveness to the opposite sex. But it's silly to see attraction as a "weakness" or "vulnerability". Many people (women included, of course) want to feel attracted in the first place, especially to someone with other good qualities - they just don't get to make that choice most of the time! That's the one sense in which 'reduced agency' could be said to be relevant - but it doesn't negate the fact that agency really is quite heavily involved in any kind of pickup.