Your investigative piece prompted me to share my views on this very crucial topic particularly in India.
One Hindu sect of Shaktipuja performs "Yoni Puja"—vaginal worship. A menstruating vagina is worshipped during rituals. Google for more information. Kamrup Kamakhya Temple in Gauhati has an idol of Devi’s menstruating vagina for worship. As Shiva's Linga Puja-Penis Worship is popular, so is Yoni Puja among some, as "Yoni" is the seat of creation, pleasure, and salvation.
You have listed some of the understandable reasons to impose restrictions during menstruation. Here, we can find some practical reasons. (1)People of limited understanding in the past considered women a reproductive machine and a menstruating female can’t conceive. (2)Due to vaginal flow, male could find awkward for intercourse.
In fact, the substance that is released during periods is the holiest because it develops into a human baby after meeting with chromosomes. If it is so, all of us are unholy. Sexual intercourse during menstruation gives immense pleasure to a female because the vagina becomes extremely erotic during that time.