Mail delegation covers "anyone can send it out" and 'there is only 1 fax number". Automatically print covers "paper automatically appears" and "don't have to constantly check the email".
What exactly are you hoping to modernize (other than "technology A has been around longer than technology B"). If it's hardware e.g. a physical fax machine with a physical line and you want to get rid of that line there are existing options to do that with or without getting rid of the fax machine and with or without changing the workflow to some other technology stack like email.
If it's "fax is insecure" I agree but until that actually becomes a problem for the businesses on the other end nobody is going to care enough to deal with the change.
Also fax's tend to be horribly insecure at the recipient end. You're not sending to a person, you're sending to some physical location, usually public, and hoping nobody loses it or picks it up and read it.
This is fairly common at hospitals (when they don't have a fax server setup) and manifests as "oh the fax didn't come through" (even though it definitely sent successfully).
What exactly are you hoping to modernize (other than "technology A has been around longer than technology B"). If it's hardware e.g. a physical fax machine with a physical line and you want to get rid of that line there are existing options to do that with or without getting rid of the fax machine and with or without changing the workflow to some other technology stack like email.
If it's "fax is insecure" I agree but until that actually becomes a problem for the businesses on the other end nobody is going to care enough to deal with the change.