Really interesting as an experiment in industrial design and a conversation piece. As a viable product, I have some doubt: anecdotally, when I see people printing documents, they're in something of a hurry, and keeping the pile of paper sheets aligned would be hard. If you slightly knock the printer while using it, the stack of paper may tilt to a side. And having to keep the papers aligned would become an annoyance similar to the PC LOAD LETTER of yore. Handling A4 and Letter sizes at the same time may not be possible. I don't know how being exposed in a pile would affect the humidity of the paper...

I like how it makes me think of printing as a computing process, paper as input and printed page as output, but instead of feeding the machine with input, you "feed" the input with a machine and it gives you the output. If you extend the thought, it's as if the machine disappears, and paper (the input) is processing and then outputting (printed page) itself.