If there's a software gap here, it's being filled as features in modern Point Of Sale systems. That space is really crowded right now (Revel, Clover, Toast, 'more modern' offerings from legacy providers like Micros and NCR). There may be an opportunity to provide a more niche offering rather than a comprehensive solution like those, but the space is far from empty.
But ok, if the fax and the phone line cost next to nothing and it "just works", then sure it makes a lot of sense.
They can (and do!) put the fax machine right by the kitchen.
It requires a lot less employee training to maintain and operate a fax machine. Can you build a better mousetrap?
If you have lots of friends in the restaurant business and am itching to get into sales, there's a cottage-industry that fits between a $50 on-sale inkjet printer, and $1000 high-end HP, but it includes on-site installation, configuration, and support.
So it's easier/cheaper for a restaurant to have a dedicated phone line for faxing (plus fax and supplies) than connect a printer to a PC?
Is this because someone needs to actually print incoming emails or orders? And if yes, is there an opportunity for some kind of software solution that would always print what it receives, with no human intervention?