While some market is there, making such a printer (hardware and firmware) would be non-trivial. Manufacturers did a lot of research to print well, and making even black and white printer of comparable quality may be very hard.
Most inkjet printers are cheap nasty bits of plastic - which is why the paper path works so badly and either jams or doesn't grab sheets reliably. It wouldn't require much engineering to build something better.
Print heads are a more of a challenge, but you can buy manufacturer originals and build a printer around them.
The firmware is a big problem, but there's a lot of research in the public domain that could be repurposed.
After all of that, you need compatible ink. You'd be reliant on third party ink clones and cartridge systems.
It wouldn't necessarily be harder than a 3D printer project, but it's not trivial, and it would be hard to make it work financially.
Given a choice between an official printer that costs $35 to buy and $60 for replacement inks, and an OpenPrinter that costs $60 to buy and $35 for inks, most people will buy the former.
