Now that everyone has email it isn't as practical anymore though. People forget or lose receipts, while it is convenient to print at home.
Not everyone wants to give out their email, though.
There are small businesses that use that Square thing on their cell phone to get paid, and I could imagine printing a receipt off your phone (especially if they're a plumber or cable repair guy and are at the customer's house), it would make sense.
Just got a speeding ticket...something like this already exist, where the trooper type on the smartphone, while the printer extension printing your ticket.
I don't find any practical use to this prototype, to be honest: For a business? A receipt printer is cheaper, both the machine itself and its accessories. A domestic use? Unless you need to print something quickly or in the act, a normal printer would be cheaper. The only plus would be the portability, but we have the Polaroid Zip already and it really haven't take off as a popular product.
im aware of an enterprise market product ecosystem that does this, though over wifi direct or bluetooth. motorola / zebra MC/TC series mobile devices and QLn printers do basically this. seen them used for inventory management and object tagging and printing AIDC codes.
tho this kinda thing for personal use, and also being kinda a niche product, sorta reminds me of CueCat, which was a PC peripheral that an old company used to send out for free around the early 2000s. it was just an AIDC code reader and the company basically tried to pioneer what would modernly be successful in the form of QR codes, that can direct a connected browser to a specific URL, so mainly for advertising purposes. unfortunately too ahead for its time and it failed commercially. tho apparently people found other uses for them like using them to scan ISBN or UPC codes and catalogue personal libraries of their books or movies/CDs.