Three Days of Impurity: Menstruation and (In)Auspiciousness
In my personal view, Indians often bullshit when common sense would be more appropriate. We could IMO avoid that.
The minute a menstruating woman sits down the blood soaks out of any clothing and stains the seat. If she stands up it flows down her legs and on to her ankles. How come no man sees much of this? Obviously most women do not desire to walk around advertising to the whole world that they are dripping blood from the very place that a man wants to put himself at any time.
I don't know when sanitary towels were invented. I know they existed in India in the 1960s - there used to be a brand called "Comfit". But I do know that Indian women often simply used rags or other pieces of cloth to soak up the flow. None of these is totally effective and most need changing several times a day at the time of heaviest flow. That means woman has to go to a private place, remove all clothing over her genitals and change.
It is not at all surprising that women who do not have modern sanitary napkins or tampons prefer a little privacy and access to an area where they can clean themselves and change. I am equally certain that a girl who first starts menstruating gets upset by the fact that she has all these things happening to her for no fault of her own. I am also certain that modern sanitary napkins/tampons which are absorbent and hold a lot of liquid are definitely a boon for all women because it allows them a degree of freedom on "those days". Women at the time of their periods - need to be vigilant and actually carry pads around in case the period starts during a social function or at work. That apart a number of women ( a high percentage) suffer from aches and pains - usually derogatorily referred to as PMT by men who don't face the risk that their pants will suddenly become wet with blood. (you need to see them when it happens!

But what about before sanitary napkins? A woman in a sari would find herself suddenly depositing blood all over the place apart from having a rivulet of blood flowing down her thighs and legs. Even wearing a cloth, the cloth could overflow any time - say when she was cooking - necessitating the requirement that she changes and washes herself again. At that time, sitting it out was a good idea. If she was performing a Puja - the same problem arose - and she would not really want to hang around. I think the rules were simply created to make it easy for women to escape inconvenient duties while menstruating.
No need to invent funny reasons and rationalizations.