The problem with ideas like this is that some entity has to acquire a pretty extensive and exclusive right of way, and it's fairly invasive to build out. These aren't like a buried cable which has a very small footprint, or utility tunnels where a relatively small tunnel carries multiple utilities. It also isn't like water/sewer, where the total ROW is extensive but only because literally everyone benefits from it many times a day.
The use case in the OP, where you have essentially a warehouse in one place and a high concentration of people who want things from that warehouse on a daily-ish basis in another place with a whole lot of people and traffic in between is kind of an ideal scenario, because they only have to make one point-to-point tunnel, and at the receiving end they can do the last mile distribution by more conventional means, or simply have the customers come to the location to pick things up.
Building out a more extensive city-wide (but far from going to every home, that would just be silly) package delivery network would be neat, but is probably several orders of magnitude beyond economically feasible. MAYBE if you were building up a new, extensively planned city from scratch you could do it as part of the municipal infrastructure, but even then you're better off putting your planning efforts and development funding into mass transit for people rather than for things. Think about it: how many delivery vehicles does it take to service a metropolitan area? How many cars would it take to get all of the people of that metro area to and from work/school/shopping every single day? Clearly getting the cars off of the road provides vastly more benefit than getting rid of the delivery vehicles! In fact if you can eliminate the vast majority of personal vehicles by offering fast and reliable public transit, then you probably don't have to worry about the delivery vehicles at all anymore.