Should women teach in seminaries?

Recently, John Piper took an utterly unsurprising position on women teaching in seminaries:
https://www.desiringgod.org/interviews/is-there-a-place-for-female-professors-at-seminary
Funny to see the shocked reaction, as if he doesn't have a mile long paper trail on these issues. Here was the funniest reaction I've seen:

As if the Patriarchy is a white Western invention. As if non-white, traditional Third-World cultures are egalitarian and non-heteronormative.
On this issue I agree with Piper in some respects, but not in others. Before getting to the main point, I'll make some ancillary observations:
i) I don't think it's coincidental that Piper is an older generation Southerner. I expect his complementarianism is largely a continuation of a traditional Southern chivalric code. I don't say that as a criticism.
ii) He somewhat overstates the purpose of seminaries. Although they basically exist to train pastors, they offer MAR degrees as well as MDiv degrees.
iii) Although he bases his position on a complementarian reading of 1 Tim 2:12, he doesn't seem to object to women wielding authority over men in principle or women teaching men in principle. He doesn't seem to object to female professors at a Christian college. Rather, his argument is geared to the nature of pastoral formation.
iv) I agree with him on complementarianism.
v) I agree with him that it's ad hoc to say women can teach men to teach parishioners, but women can't teach parishioners directly.
vi) He oversimplifies pastoral ministry. A pastor of a small church does everything. By contrast, megachurches have compartmentalized ministries. Due to the size of the congregation, the ratio of pastor to parishioner, and the financial resources of a megachurch, what one man must do singlehandedly when pastoring a small church gets delegated to several different ministers at a megachurch.
That complicates his complementarianism. Take visitation ministry or a woman's Bible study.
vii) Does Piper think it's permissible for a pastor to read a commentary by Karen Jobes, but not to attend a class by Karen Jobes? If so, what's the essential difference?
viii) A good pastor doesn't necessarily have the same skill set as a good seminary prof, or vice versa. Seminary professors can outstanding scholars or thinkers, but abysmal communicators. Likewise, great scholars and thinkers may be sorely deficient in social skills.
ix) Now I'd like to get to the main point. I disagree with Piper's position on this particular issue. The rationale Piper gives for his position is unwittingly at odds with complementarian anthropology. Sophisticated complementarians aren't voluntarists. They don't think Biblical gender roles are arbitrary social constructs. Rather, they think these mirror stereotypical physical and psychological differences between men and women.
Yet Piper unintentionally acts as if these roles are interchangeable. He thinks that if male seminarians view male seminary profs. as pastoral role models, and if you put a woman in the same slot, then male seminarians will view women as pastoral role models.
Which ironically assumes that men relate to women the same way they relate to men when women occupy the same social role or institutional position. But I find that highly dubious and contrary to complementarian anthropology.
In my observation, men measure themselves by other men while women measure themselves by other women. Men don't measure themselves by women and women don't measure themselves by men. The psychological dynamic between men and women is different even when the social roles or institutional positions are artificially the same.
That's one reason we defend heterosexual marriage. Mothers can't take the place of fathers while fathers can't take the place of mothers. Kids need both. One person can't successfully play both roles.
The father/son dynamic, mother/son dynamic, father/daughter dynamic, mother/daughter dynamic, brother/brother dynamic, brother/sister dynamic, and sister/sister dynamic are all different.
Suppose the military put a woman in charge of a Navy SEAL team. Would the male members of that team relate to her the same way they relate to a male comrade just because she was given the same position? Are you kidding me?
Another example is the difference between male and female hymnodists. Male hymnodists have a different sensibility than female hymnodists.
I think it's wholly unrealistic to suppose that if a normal man has a female seminary professor, he will view her the same way he'd view a male seminary professor, as though male-on-male psychology is transferable to male-on-female psychology. This is not to deny that men can look up to women, and women can look up to men–but it doesn't mean they're consciously or subconsciously thinking that a member of the opposite sex embodies what they aspire to be like. That's just not how human nature is wired. Women are not an example of how to be a man. Men are not an example of how to be a woman.
There are, of course, some generic virtues they can share in common. Some Christian women exhibit perseverance in adversity or even moral heroism. We can admire that in members of either sex. But by the same token, that's not a lay/clerical distinction.