I think the idea is that this is eventually built right into the products. The washer with the built-in Amazon button for detergent, etc.

That's an interesting thought. There would be deals by detergent companies to include their button in a washer. Also maids could order the products themselves if they're responsible enough.

I'm thinking more about P&G giving you a free washing machine if you agree to automatic delivery and billing of their detergent.

You can certainly choose other brands to put in the machine, but every 40 cycles another box of Tide Pods will show up on your doorstep.