And here is the problem. What actually happens is the people who control "production" end up with most of this extra money.
This is not true. It's actually a pretty well-understood economic phenomena.
When changes to pricing is forced by changes in upstream costs, as with this example, but also as forced by increased taxes/fees, etc., you can predict who will bear the brunt of the cost (or enjoy the windfall) based on the elasticity of the buyer.
For example, we know that the elasticity for gasoline is very inelastic, because consumption only changes a small amount in response to price changes. This means that an increase in taxes on the petroleum industry will be borne mostly by the consumer, and not the producer.
However, for other industries where consumers are more likely to change their spending habits in relation to price changes, it will be the consumers that are on the winning side.
Lowered cost of production always results in lowered cost of goods, which either raises quality for the same price, or lowers cost and released cash for other purchases.
And to avoid even more problems the delivery network could work with post offices to put these safes in place of P/O boxes. Australia Post already does this - you receive a package and they send you an SMS with the code to unlock the safe they've left it in. The delivery truck would just put the packages in the safe totally autonomously.
The safe idea is interesting, though.
It's a somewhat different experience to a human knocking on your door, but I'm sure it could be made to work.
Automated delivery vehicles may be able to do better in terms of offering a choice of delivery time, and sending accurate estimates of arrival time. There's considerable scope for doing a better job of delivering to households where there is usually nobody home during "working hours".
What you're essentially describing is a motorised set of po boxes. Which would work brilliantly. For pizza delivery it's a motorised warmer oven with multiple components, probably looking a lot like those little motorised droids that are always zipping around the ankles of actors in Star Wars films.
But delivery trucks will still need someone in them to make the deliveries. But what would change is that the delivery person could be doing things in the truck while on the rounds - this could be related or unrelated work.
Generally, if a technology transition releases a lot of productivity, it also drastically lowers cost of whatever is affected (delivered goods, which is everything). This, by rights, should free up a lot of extra money for people, which they can then spend on other things. The other things generally cause more economic activity somewhere else, which should create the new jobs.
But a portion of truck drivers will lose their job, with it never to return.
However, this can't be, nor should it be, stopped.