Although it’s inexplicable, there are still some people and institutions who prefer to send hardcopy documents rather than electronic ones (Only a couple of years ago, the Law Society of England and Wales, for example, declared itself to be ‘against email’).
This means searching for a post box and ensuring that the right stamps have been applied. After that, you just wait for some response (assuming no postal workers’ strike that week).
Today’s invention is an alternative way for the Great Unwired to send hardcopies to each other.
Banks are still reasonably trusted institutions (if you ignore all those missold pensions, Nick Leeson, sub prime mortgages…). They have ubiquitous ATMs which are capable of handling deposit envelopes and a secure way to gain access to and, if necessary pay for, their services.
People wanting to post a letter could write it as normal, print an address on a deposit envelope and enter that into their local ATM. The content could be automatically extracted, scanned, identified from bank address records and sent electronically to whichever ATM the intended recipient used next. On logging in with their pin, the ATM would print a copy of the document, insert it in an envelope and drop it into their hands.