Water and gas are delivered by 'tunnel' and they seem to work just fine. If you think of this as a refinement of that, then it makes a lot more sense. If they need to dig human-safe tunnels, then yeah, it's going to get expensive, but a "fat pipe" network seems pretty simple. The things that go up and down oil pipelines prove that we can have machines in pipes doing jobs for us, so I'm sure moving some boxes around is quite possible.
That said, I seriously doubt we'll all have a chute outside our house where we drop off or collect things. I guess the local shop might have one, but even then I doubt it. Some sort of depot network could work, and I guess each depot could be small so long as there was a hulking big warehouse somewhere nearby. The thing is, you wouldn't want to rent your depots because you can't move to alternative premises if the landlord jacks up the rent, so that means buying property which is expensive (at least up front). It could scale, but it's got a huge upfront investment and as Doddle (https://doddle.it) are finding, the 'depot' model isn't actually all that compelling and competing in a market where price is king isn't easy.