I'm very much in favour of the postal service, but I don't think you're being fair in this comparison.
To operate a postal service, you need a lot of sorting offices and service points (postboxes, post offices, letterboxes). Unless you have this infrastructure, I'm envisioning a postal service with a maximum capacity of whatever all its employees can hold in their hands at one time.
And you need an addressing system and/or lots of people familiar with the local area, otherwise delivery is too unreliable for use.
And you need an internal police force to stop your own workforce stealing people's goods -- the employees "with a pulse" but not "a lot of education" are especially bad for doing that.
Meanwhile, in remote African villages, you buy things at the shop by sending a text message like "pay 32.10 to 67319" on your Nokia 3210 from 1999. It texts the vendor confirmation, it texts you back a receipt. The phones are battery powered, you charge them with a solar panel or a hand crank. The radio masts (and backend servers) that power this service are sometimes lacking electricity, but you just learn to go shopping when there's signal.
Certainly, it wouldn't be easy to get back to having Nokia 3210s if some kind of global destruction happened. But the same is true of pen and paper -- we need industrial levels of production for paper, ink, pens (or quills), and good storage, for paper-based record keeping. Before that, we used cuneiform on clay tablets... I think we can assume that we'll keep our ability to manufacture basic ICs and remember how to do radio communication, we won't ever have to revert back to pre-Marconi days.