Where to start....Oh yeah, not going to happen.
Not necessarily because the tech isn't there. In fact, it's possible now.
The reason it won't happen is because it doesn't make any sense.
Why does somebody buy from Amazon in the first place? Most likely to save a few bucks compared to the local store. Another reason may be to avoid going out or to find something that is harder to find.
The premium for a 30 minute drone delivery likely makes it more expensive than taking a 30 min round trip to the store and buying the same thing. Including your gas. And what do you think is cheaper for Amazon themselves, operating an expensive drone, or shipping UPS, FedEx, USPS? Shipping at their reduced rate is most certainly cheaper. So what's the point of all this?
After above's point, we don't even have to look at all the logistical problems this faces. One example being that GPS isn't accurate to the point that would be needed. GPS is good within about 25ft or so. How could we expect this dropped in a proper location near someone's front door? Would need far more advanced tech beyond GPS. The problems are endless.
Others have discussed all the possible criminal acts against drones and their packages. That's a given. Then there's all the possible accidents. A compromised drone falls from the sky and lands on a child's head - kills child. Then what?
Think about it, shipping their massive volume is cheap enough that they offer free shipping to their customers who spend just $35. Why build a multi-billion dollar system to offer an unneeded service?