This is obviously part of Amazon's effort to build out their own delivery network in order to muscle out fedex, ups, usps, etc. If their drivers aren't delivering packages they can be delivering food. That makes their whole delivery network stronger because it allows them to have more drivers employed driving around town all the time. It's the same reason Uber got into food delivery.
Does that mean your food delivery depends on the package delivery schedule? "Sorry your pizza is cold but we had to deliver a TV first." For myself, I usually prefer to just go and pick up myself; that's almost always the fastest option.
It's not about being the fastest, though, it's about being more convenient.
And even fastest depends on the area. Where I live (near a city centre) I can chose among 300 restaurants from a centralized meta-ordering service, and have their food delivered in 20-40 minutes.
It will take me 20 minutes to even decide to get up, find my keys, drive around, order and wait for the food.