My thoughts are much less about tradition. I personally think that (aside from the speakers) the women's meeting should just be for women, and I'd like to see a sister speak at a PH session someday. But I don't think they should be combined (yet) because we as men (& young men in particular) in general aren't ready for it.
We have loads of research of the effects of the male gaze on women and in the LGBTQ community. Essentially, men are conditioned by society to affect the space around them in a way that establishes/secures their masculine identity; which in turn puts pressure on others (particularly women) to adapt to that presence. By keeping men out of the women's meeting, we allow our sisters one brief moment where they can be assured that no men will be asserting their socialized dominance - even if that assertion is entirely unintentional. No arms around a spouse/significant other to make single sisters feel insecure/inadequate in a church already very emphatic about families, no single guys "window shopping", no pressure from men to look, react, behave, etc in any particular way. Studies have shown that having a socialized male presence influences the behavior of women, and I believe the inverse is also true.
On the flip side - and where I'd like to do more graduate research myself because there really isn't much - there is also a change among men's behavior in the presence of women. We are less likely to express emotion, more concerned with appearances, and (having been taught by our culture this way) very easily distracted by any source of potential female attention. In my opinion, women are not barred from PH session attendance because we don't want them to crash the party; men (still speaking generally) are still so bound to social conditioning that having a place free from a majority of those hyper-masculine societal pressures liberates us.
We first need to come closer, if not fully realize, the social, political, and economic equality of the sexes. Then we can shatter the glass ceiling from both sides, root out rape/objectification culture from our collective subconscious, and allow men to feel a full range of emotions without the fear of stigmatization. Until men - ESPECIALLY young men - no longer have to live in fear of being perceived as feminine (aka vulnerable, weak, sensitive, and every other trait that patriarchal society has deemed inferior), we will not be able to open ourselves to the full spiritual potential of our meetings. We need a place to feel the spirit free from those pressures, which will hopefully spill over into a realization of how EVERY meeting could be if we eliminated the pressures altogether.
Sorry if that got wordy. TLDR: Patriarchal socialization has made men prisoners of their own oppressive social structures (on top of the cavernous disparity faced by women every day). Until we get rid of those for both men and women, we all need a place where we can experience a life without the male gaze or rigid masculine "ideal"... Even if it only lasts for 2 hours. In my opinion, I think we could 1) Tell guys not to attend the women's general meeting - and encourage them to do everything in their power to facilitate attendance for the sisters in their lives, 2) have a sister speak at Priesthood sessions, and 3) work to change society so that my kids will one day not have to worry about the social pressures that make the division seem necessary/reasonable in the first place.
