I'll restate what I think the essential characteristics of facsimile are. Facsimile is a particular form of communication. What you want is differentiation from other forms of communication, for some reason. This is just a very weak statement.
Facsimile terminals can always be available for transmission or reception.
The sender will have some knowledge that delivery was made to the intended recipient. Some terminals are shared, etc. I am not sure that it allows for PDFs since they only give you an approximation. Now I'm not arguing that facsimile is the best mode of communication. All I'm saying is that there are millions of people out there using facsimile using millions of terminals and they have certain expectations.