> why fax is still being used; what problems fax solves.
You give someone a telephone number, then you hear a noise and a document magically appears.
Sure, there's software solutions. People can email documents to an email address, and your computer can automatically send it to the printer. Unless your computer is off, or the app isn't running, or someone queued up a hundred pages in the printer, or the printer is out of ink, or the person sends you a file in an incomrehensible file format.
These issues are all solvable, but it's less effort to buy a fax machine and plug it into a phone line.
People know the reasons why faxs suck. What they're not so sure about is why fax is still being used; what problems fax solves.