Yeah, my work fax can also send documents to my email as pdf files.
But to your point, documents can be doctored before being emailed.
Fax to fax shows that the file was not doctored in between the scanning and transmission process. Faxes also give the sender a confirmation sheet saying whether the document transmitted correctly or not, and to what number. This provides you legal proof that you sent the document, should you need it.
Most recently I have used one when I lost my proof of driver's insurance and the insurance company faxed it to me at work so that if something happened while I was driving before I got my new cards I wouldn't get arrested for not having it.
I've also had a few employees on my staff need to use our fax machine for health insurance related stuff.
Honestly, for personal reasons I can't say I have ever used a fax more than once a year.
For business however, often our clients will need something from us but they will be on the road or in a conference room with their laptops, and not be connected to a printer. While they could get the email, they have no way to produce a hard copy right now, so faxing it to the nearest fax machine basically works like us remote printing on their printers.