While I can certainly see the point he's making, most businesses have had large copier/printer/scanners that can send pdfs to a CIFS share on the network, e-mail pdfs via SMTP, and send faxes for years and years. These copiers typically come with the upgrade after rentals, and there are lesser $50-$100 inkjet home versions for smaller offices as well. A lot of companies do what the author posted and don't have fax machines.
But the main issues aren't signatures or other things mentioned at all: they're human factors and cost factors.
There are two on the sending of faxes:
1. Large and bureaucratic companies still have procedures from the mid-1990s that explicitly list faxes as the method, and it's a mess to get anyone to fix it. No one will disobey these procedures, as it's often a punishable offense.
2. There is rarely any proper setup, much less the required training to end faxing and go paperless. Whether management, IT, or the copier company should do it is irrelevant. No one seems to wish to invest the necessary time for proper training, particularly if there are dozens of facilities and hundreds of office employees.
And two on the receiving of faxes:
3. People will balk on relying on e-mailed pdf's simply because there is a threat of it being lost to a spam filter. These spam filters often can't automatically choose well between a fax and an e-mailed, randomized PDF selling bootleg pills. One important fax lost and all trust is gone. Fax machines don't have this problem.
4. Fax machines often are still used simply to receive, but not always to send. If you are expecting a fax, only faxes will come out of a fax machine. It won't get confused with the dozens of other pages in the big printer/copier device, much less end up with piles of nameless pdfs in a CIFS share.