This could be the natural next step for one click shopping. Obviously it'll be more difficult without textual or visual capabilities, but things like "Add gelato to my shopping cart"(as apposed to shopping list) would be huge for Amazon fresh shoppers and other products that aren't too ambiguous.
Another application: "Alexa, order a Dominoes pizza with extra anchovies. "
The two main things I use Siri for are setting alarms ("Wake me at 7 tomorrow") and adding things to shopping (i.e., reminder) lists ("Add pasta to my Costco list").
It'd be kinda magic if I could say "Alexa, get me some toothpaste" (and have it know that I like Mr Sparkle Minty Fresh) and have that turn up on my doorstep the next day.
And I guess if it's always listening, it could build up a 'map' of when you're home. So it could schedule delivery of fresh stuff for when you're likely to be there.
It still requires a jump to the pc to order; but no reason they couldn't add a way to initiate an order from it. It's also a tad less privacy intrusive then echo.
Another application: "Alexa, order a Dominoes pizza with extra anchovies. "