I haven't tried using Alexa to order anything but in my mind the problem here is the Amazon market itself. You can't guarantee that you will get the lowest price and that the seller is "reputable".

And consider things you want to reorder like dish soap or some other consumable (diet coke maybe). Do I get something unexpected? Or do you have to fill your Amazon Pantry order.

Some people use Alexa to create shared shopping lists or a shopping list so. I think there could be some innovation there where amazon post-processes it for deals etc... not sure if they do that.

Also the Amazon website itself is just a mess. Customer support is hard to find. They really have a ux problem.