Well the only problem here is that general delivery is still not eligible for any of the main things people need an address for, like ID, tax docs, etc. Even if you want to pay for a PO box (which also doesn't satisfy those requirements), you need an address to register for one.

I really wish there would be more work to try to at least add some kind of alternative path here, given America's growing homeless population. Leaving things to the goodwill of family or friends seems to me like a dereliction of duty by the state.

The post office would identify you on access and hold mail for an appropriate amount of time.

Like for some deliveries you need to sign a receipt that will be legally binding, the post office would take the role of handling those.