I have no idea about the technical stuff (I can’t really decipher your second paragraph), but there is a legal advantage for fax machines.
Emails don’t count here as “ in writing“, so if something needs to be in writing you need to send a signed letter - or a fax.
Fax is like a signed mail, but In almost real time. So if you send legal relevant stuff, you have proof what you sent and when the receiver got it.
However, you talk about Encryption, I don’t know if E-Mails can be encrypted, fax are definitely not. They go through a normal landline with those beep tones similar to a normal modem made when dialling into BTX or the early internet.
Google.de für suche
Deepl.com für Übersetzungen