I never really got the point of them since they were usually for things that stored really well and get used up at a relatively constant rate so it's usually not a surprise when you run out, so like why would I need to rush and blindly push the button to buy more detergent/toothpaste of a certain brand without knowing the price when I'd just eventually buy it in my normal shopping run/order.
The goal was to reduce friction in the purchase. You had to walk to a computer, bring up Amazon, look up the product, click the version of it you want, and push "one click order" (or maybe two or three more clicks) -- that's a lot of opportunity for you to just add it to your shopping list and just buy it at the grocery store. Or from your point of view, that's a lot of effort for a product that you already know you…
You don't know if the toilet paper is going to arrive the same day, next day, 2 days, or 2 business days. Many times if you know beforehand it's going to take 2 days to get toilet paper you'd just run to the grocery store instead.
Not just toilet paper -- even with shampoo, body wash, kitchen soap, laundry detergent, kitchen sponges, I'm usually unaware I'm running out until it actually runs out, and with most of these things I can't wait 2 days. I also live 2 blocks from a 24-hour Safeway so it's not actually an issue.