Two of my siblings were raised in cloth diapers due to our finances in those years. A clean butt isn’t difficult to achieve cheaply. It just requires getting a little more dirty than normal.
Which only shifts the demand to soap and other cleaning products.
Lye and fat and salt makes soap and glycerin. Should lye run out you can make it from hardwood ashes. Should salt run out you can make it by evaporating sea water. Mix glycerin with alcohol to make hand sanitizer.
Have you tried getting hold of isopropyl alcohol (or similar) recently? Impossible :(
A pot-still seems like a doable weekend project.
Soap and detergents are denser and therefore easier and cheaper to transport. So then thanks for the supporting point I guess.