A cheaper option (if we’re going to do away with the restriction that the post card should be sent by the sender) would be for the recipient to hook their printer up to the network, and just send bits. It is better, actually, you can even scan a real hand written post card.
We could even make a standardised protocol, where anyone could send messages to any connected printer: like letters, except a facsimile of the original document is produced. I'm struggling to think of a catchy name for this, though.
It’s not a fax unless it’s from the facsimile region of france. What you’re describing is just sparkling email.