It's really surprising we have open source 3D printers with way more complex kinematics, parts, etc than a printer but we don't have a traditional open source printer despite printers existing since the 70s.
Aside from making a pen plotter, it would be very difficult to make an open source 2D printer. A 3D printer is an enabler of this, but I would think to be feasible you would have to at least find a popular "business end" of the printer to reuse. There is a project called "openprinter" that is attempting to make an open source inkjet printer but it's really early days.
It's been on HN this year to my recollection. Maybe it has some closed firmware or something that means it's not "open" for you?