WIY says (perhaps jokingly) that the short ones are there to help the men look. My understanding is that when there’s a machlokes regarding a new mechitza, it’s often the women who argue for a short or transparent mechitza so they can look (presumably at what’s going on, rather than at the men). I know my wife likes to daven in a shul with a balcony so she can see what’s happening. A balcony seems to be the ideal solution, but very few shuls are built with one these days.
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