> Scan with random app, send with any of the various pdf-to-fax services?

Looked into it...so many of them want you to subscribe or have a stupid pricing scheme.

> As for the why... faxes operate over the legacy network using an acoustically coupled modem.

There's nothing special about a fax connection. It's just a telephone line (which my phone has). The "modem" part could easily be done in software. All it has to do is synthesize the right noise on the line.