If you have a scanner it's actually quite painless even if done frequently. That's what I did when my old standalone fax machine quit on me and I had to get some faxes out. Phzzzzzt ... clack ... -> Type in number -> Send.
Now I have one with a sheet feeder and its own built-in fax machine, much easier.
The, one fine and sunny day, "Cannot connect to server".
Just as a side note: There is some stuff I and the other party would most definitely not want to go through numerous unknown email servers. The phone network is a whole lot safer than the Internet. Heck, sometimes you don't even know for sure via which countries your email might get routed.