>> But why do you need a specialized button that only does that? That's the part that makes no sense.

It -does- make sense if you take it as a way to introduce not a product ("specialized button") but a platform[1] for long overdue and much needed innovation that some very influential people have started to fund and promote[2]. It is not the only way to do it, but it is amazon's way to facilitate it and in the process get some market pioneering advantages. A company like amazon doesn't have the infrastructure to start building home appliances but it required little effort for them to contribute in a way that brings them great benefits. Smart move, amazon.

[1]: https://www.amazon.com/oc/dash-replenishment-service [2]: https://www.quora.com/What-is-the-future-of-food-delivery-1/...