Canada Post's community mailboxes have oversized slots for packages, which work on exactly the model you propose. I gather it works reasonably well.
On the other hand, I have absolutely no desire to have random delivery staff wandering in and out of my apartment. If that means I have to shop for my own groceries, rather than having them delivered, then that's what I'll do. This also has the benefit that I can pick my own produce, rather than relying on someone who works for Peapod or similar, who likely gets paid rather poor wages, and who, to pick one particularly memorable example, has no particular interest in seeing to it that I get fresh, firm, ripe bell peppers instead of sallow, sunken, half-gone-over ones.