It depends on the threat model. If I need to prove to a court in the US, then I'm signing paper and faxing it. To do it differently would be more expensive to prove.
I'm talking about the technical sense. Where there is no encryption at all, anyone with a phone line splitter can listen in, and the machines are usually not in a secured area so anyone could just pick up the fax and walk away. Not secure at all.
dd36 and swixmix seem to be taking the other side of that argument.
For the threat model of a physically local attacker with either the right timing (for grabbing an incoming fax) or the right knowledge (for the phone system equivalent of tcpdump), you're quite right that fax is insecure. Likewise for state sponsored adversaries or certain organized crime groups.
But if you just want to make it hard for people scanning the internet to see what juicy corporate espionage they can find and resell, without specifically targeting you, fax is probably less vulnerable to that threat model than, for example, an undermaintained email server. Likewise if you piss off script kiddies somewhere on the internet with botnets and exploit kits, your website is probably a bigger risk than your fax machine.