It's also a (moderately) higher barrier to entry, so it's less likely to be aggressively used by heavy-handed copyright holders.

Though in practice, fax has turned into this bastard child of excessive analog-to-digital conversion, at least among newer companies. Senders email their attachment to an email-to-fax service, which sends it over POTS to a fax-to-email service converting it back into a PDF and emailed as an attachment to the recipient.

If a company sells both services (hardly unusual) and a client of theirs sends a fax to another, I wonder if the system calls itself... ;)

Based on my own experience... yes, at least to start. Depends how easy (and fast) it is to detect that both parties exist within the network.

Really? I can't say I have experience building such a system, but to me it seems the solution has already been built: fast off-the-shelf DNS servers, using phone numbers as virtual (sub)domains.

My experience is in the context of payments - when charging someone's payment card, check whether it's one we've issued and just run it as an internal balance transfer rather than run it through Visa (read: free). When doing the whole "build fast, iterate quickly" thing, it's easy to forget about such optimizations, especially when it's a relative edge case and works just as well if you leave it alone (arguably better, since there's less conditional logic in the code)

So by "network" I more meant database (i.e., network of users).

Also, there's one workflow which is still easier by fax than email: receive it, physically sign it with a pen, send it back with the signature.

Have you ever used Preview that ships with OS X? There's a signature button in it... It's ridiculously simply!

I recently refinanced my house, and realized that there was a potential for a LOT of this sort of thing. So I paid the app store a few dollars for a PDF modification program, and just put a shortcut to a scanned signature of mine, and added that in the right places. Requested the documents as email instead of fax, and emailed them back. Totally acceptable and saved a bunch of time (in waiting for the printer and scanner) and money (in paper and ink).

HelloFax is great for this as well.