I wonder why we don't have any open-source printers...
I'm sure part of it is that open-source hardware in general is "harder" to do than software, but perhaps there is something more to it... such as people generally not wanting to invest time creating a more-crappy version of a black box that already does it's thing well enough. Perhaps it is only after printers get significantly worse or more annoying that people will start investing their own time creating alternative firmware/hardware.
It probably hasn't caught on because when it comes to consumer inkjets it isn't the printer that's the expensive bit. Compare to 3d printers where the medium is fairly cheap and reasonably interchangeable. And if not inkjet then laser, and laser toner is really nasty stuff to work with.
Tank style printers would probably be the way to go for ink, since the print head is not a 'consumable' part. For laser, maybe pick a popular proprietary toner cart and design around that?
Most likely the printhead is the problem. To be able to sell those at low cost, you'd have to make a lot of them. But to start a production like that would take a shitton of capital which a startup doesn't have access to. And HP&Co. won't sell you printheads because they don't want competition.
Well... it's something, and since the output is on conventional printer paper, I think we have to allow it. The mechanism is less important than "can I hand it to answer an assignment" (which this passes, as opposed to turning in a 3d-printed plastic tablet or something).