It's all about the signature...
We fax documents all the time. Documents are signed in our office by our clients and ourselves and then faxed to insurance companies, banks, lawyers, financial institutions, etc. Due to compliance regulations, all documents get approved by one of a small number of people and then faxed from one central fax machine. This fax machine not only faxes the documents to the recipient, but it automagically sends an image of the fax to a centralized storage server for archiving purposes. The paper copy is also filed and eventually sent off site for hard copy archiving.
To do this via e-mail or e-fax, we would have to set up a centralized scanner, either networked to the PC's of the operations staff that actually does the faxing, or attached directly to a centralized PC - which would have to be set up with individual accounts for each person in operations since compliance rules don't allow anybody to do anything under a shared userid. The operation staff - not the most tech savvy group around - would need to understand how to access the documents, address them correctly (is it an e-mail or an e-fax?) and then send them. They would also have to receive documents, print them out and distribute them. Since we send and receive dozens of multiple- page documents every day, there is way too much chance for errors.
Somehow a single machine with a simple numbered keypad just seems so much simpler - read: idiot proof - for sending and receiving documents.
Maybe that's why they've lasted so long.