This should not be the customer's problem. If you are doing drop shipping, then you need to factor in the background logistics.

If I buy stuff online, then I (as a customer) really want to have only ONE delivery from ONE place. If I have to wait about at home for 3 days, waiting for several deliveries, I will not be happy.

Also, you just multiply the things that can go wrong.

Again, like your other idea - nice in theory, horrible in practice.