Software modems used to be common and how many people connected to the internet. They didn't work as well as hardware modems but they did work. there is no reason a modern smartphone which has a much more powerful CPU couldn't do a software fax (smartphones also have a GPU which is possibly even better for this type of processing). IIRC the fax protocol is pretty dumb/simple so it seems like it shouldn't even be difficult - though I don't need a fax often enough to bother to try.

> 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.