Sheet-fed scanners are ridiculously expensive
I don't know that I'd say ridiculously expensive... Sure, they cost more than a generic fax machine, but not that much more. And you often get what you pay for - meaning a more expensive document scanner will likely hold up better than your bargain fax machine.
And then there's the real multifunction devices...
plus you have to save the file, attach it to an email
Any place that's dealing with a large volume of paper - be it scanning, printing, or faxing - really ought to have a good, solid all-in-one device. Not one of those piece-of-crap inkjet things that HP sells for $100 - but a real office machine. The kind of things that Kyocera or Canon make. The big beasts that'll scan in reams of paper in just seconds, automatically convert it to whatever format you want, OCR it, and then store it somewhere on the network or email it or whatever else.
These things really aren't that expensive. Usually you can get them under contract with some local company and then you don't have to worry about maintenance or anything. And the cost per page is usually much lower than it would be otherwise.
These things make scanning insanely easy. And they'll also email for you - making the whole process just as easy as sending a fax.
then, hopefully, the file isn't too large for the sender or recipient's mailserver.
I guess it depends on where you work and what you're sending and where it's going... But a PDF document isn't that big. I've got 100 page documents that are just a couple MB. Most folks can receive files of that size.
Plus, it isn't like you fax machines have a magically endless supply of paper. If you're sending a document that's big enough to worry about the size limits on their mailserver, then they're going to be going through a lot of paper. Better hope they filled it up before you sent the thing.
With the fax machine, one just drops the stack in, verify the fax successfully transmitted, task complete.
Ideally, sure, that's how it works. But I can boil down sending a PDF attachment to something just as simple.
What you're neglecting to mention is that the entire time you're sending your 100+ page document, your fax machine (and attached phone line) are busy and unable to do anything else. As is the recipient's fax machine and phone line. And if you're sending (or receiving) a lot of these things, you can tie that line up all day long. Which is exactly what we were doing here.
Also, many people feel that snooping of phone lines is much less likely to occur than snooping of email, when is sent in the clear.
I am always amazed that folks think a fax transmission is somehow secure, and simultaneously seem to believe that securing email is an insurmountable challenge.