“Shas and United Torah Judaism seem to be utterly disinclined to have any.”
Interesting that you ask now. Two days ago, the Daf Yomi included the words that it’s a man way to conquer but not a woman’s.
Here is something I found online:
Here is a summary of the halakhic literature based on an excellent article by Rabbis Aryeh and Dov Frimer in 2007. In the book of Devarim (17:14-20) the Torah states the laws of appointing a Jewish King. The Midrashic commentary the Sifrei notes that the Torah mentions the word king three times. From the fact that the word king is mentioned three times we must learn something new each time it is mentioned. One of the three things learned is that you may appoint a king – but not a queen.
The Rambam codifies the halakha as follows. “We may not appoint a woman as king. When describing the monarchy, the Torah employs the male form of the word king and not the female. This principle also applies to all other positions of leadership within Israel. Only men should be appointed to fill them.” (Hilkhot Melakhim 1:5) The question we have before us is what is leadership or in Hebrew “serara”? Serara can be understood to be anyone who makes unilateral decisions. There are several rishonim (medieval halakhic decisors) such as the Hinukh, Rashi and Ran who disagree with the Rambam’s interpretation. They limit the scope to just a woman becoming a queen but they allow for a woman to have a leadership role. “
Besides the above halachic issue, there is also a tsniut issue.