If women are holier than men and naturally closer to Hashem, which is why they aren't obligated in as many mitzvos, why is there at its least a minhag and at its most a prohibition barring them from positions of leadership? On the contrary, wouldn't it be more appropriate for them to be consulted on matters of growth and hashkafas hachaim.
Women are in positions of leadership all over the Jewish world generally.
I think that when you say "leadership," it commonly means Rabbinate or high position in a synagogue.
This is a massive misconception because the home is a holier place in many ways. Synagogue is not the center of Judaism, but the home is. And the mother is the leader there.
Women are compared to a sefer Torah. So you may not always see it in the public but it is the wisdom, intelligence and passion behind the entire Jewish world since its inception.
In chesidus we also learn
The body is holier then the soul
On when Yakov, the neshama, men finish the avoda (moshiach comes) then also in this world we will see the same hierarchy
As it says in the posuk regarding the world to come isha tsovev gever
But for now the word is upside down what is above higher bellow is lower, and what is higher bellow above is lower below
For now woman are lower and do not rule men, but couse men to grow by receiving from them
Fascinating question! In Rav Hershel Schachter's article explaining why women Rabbis isn't advisable (to say the least):
One aspect of Elokus is the fact that Hashem is a "Keil Mistater", He always prefers to hide b'tzinah. Therefore we assume that part of our mitzvah of preserving our tzelem Elokim is for all of us to lead private lives. The prophet Micha (6:8) uses the verb "leches" in conjunction with tznius: "vehatznea leches im Elokecha." The rabbis of the Talmud (Sukkah 49b) understood the choice of that particular verb to be an allusion to the expression in Koheles (7:2) "tov laleches el beis ovel mileches el beis mishteh." This particular form of the verb appears in connection with a funeral and a wedding - occasions which are intended for a public outpouring of emotion. The navi Micha is telling us that even on these occasions one should tone down his public display of his inner emotions. And kal vachomer - so much more so all year long, one should try to lead as private (as tzanua) a life as possible.
Sometimes the halacha requires of us to act in a public fashion (b'farhesia), for example to have tefilah b'tzibur, krias haTorah b'tzibur, etc. On these occasions the halacha distinguishes between men and women. We only require and demand of men that they compromise on their tznius and observe certain mitzvos in a farhesia (public) fashion. We do not require this of women. They may maintain their middas hahistatrus, just as Hashem (most of the time) is a Kel Mistater (Yeshaya 45:15). Of course, if there are no men in the shul who are able to lein and get the aliyos, we will have no choice but to call upon a woman, and require of her to compromise on her privacy and lein, to enable the minyan to fulfill their obligation of krias haTorah. If there is a shul where a woman gets an aliyah, this is an indication that there was no man who was able to lein, and this is an embarrassment to that minyan. This is what the rabbis meant when they said that a woman should not lein - for this would constitute an embarrassment to the minyan (Megillah 23a.)
Can women be incredibly insightful role models in middos, hashkafas hachaim, bitachon...absolutely! Does that mean those women must compromise their tznius? Absolutely not! Countless women serve as mentors for so many future wives and mothers of the next generation. I have personally seen a few Roshei Yeshiva strongly consider their Rebbetzin's input when deciding certain difficult life questions for other people. This isn't even including the women throughout the various communities all over who have provide shiurim and discussion groups for other women - certainly "matters of growth and hashkafas hachaim" and more. These wise women are advising many people in these areas, just not necessarily open to the public eye.
In Maharal language I think you would say men are tzurah, women are chomer. Leadership is the provision of tzurah to the klal so cannot be provided by women unless they become masculine to some extent which is a perversion of their natural order.