No reason businesses couldn't receive a code when they incorporate, and you'd presumably allow homeless people to set their location as their local post office for pickup (just like they have to do currently, I'd imagine).
The problems with the existing system are not insurmountable either.
This proposal, which isn't going to replace the geographical based system, ends up greatly increasing the number of issues, for seemingly little gain. Each objection, and proposed solution, is an example of why there are issues.