A lot of the products seem to be small household items, like razor blades, trash bags, water filters, and the like, that when you run out you are (1) probably going to want to replace with the same brand, (2) probably don't want to put off replacing to wait for a bargain, and (3) probably will still buy even if the price is a little more than the last time, but within the normal Amazon price variation.
Also, according to their documentation, pressing the button queues the order and sends you an email, which includes price information. You can cancel the order before it ships. I'd expect that the normal flow for most people is to press the button when they notice they are running out of something, and then check the order details when they next deal with email.
This seems incredibly non-optimal on a few levels.
I rarely buy small household items at full price, just wait until my brands go on sale or I have a coupon to buy several. They go on sale often enough that I almost always have items in the house. I probably have a five year supply of razors at my house, they take up basically no room. If I need something right away I'll put it on the grocery list and pick it up next time I go to the grocery store.
On top of that I don't really believe in shipping my household products to me one by one, seems very wasteful and inefficient. Plus you'd either need to pay extra for shipping every item you need or buy a prime subscription on top of that.
Amazon pricing is all over the place, not like the normal variation of other stores. You could easily be paying double or even triple since the last time you bought.
Also, according to their documentation, pressing the button queues the order and sends you an email, which includes price information. You can cancel the order before it ships. I'd expect that the normal flow for most people is to press the button when they notice they are running out of something, and then check the order details when they next deal with email.