The hardware precision is the hard part, along with speed. Most hardware parts wouldn't be hard to get because most of the printer is just motors, rollers, etc, but the print head itself is the part that would be the hard part.

https://computer.howstuffworks.com/inkjet-printer.htm

Here's a good reference, from that website describing thermal bubble which is the more common technology;

Thermal bubble - Used by manufacturers such as Canon and Hewlett Packard, this method is commonly referred to as bubble jet. In a thermal inkjet printer, tiny resistors create heat, and this heat vaporizes ink to create a bubble. As the bubble expands, some of the ink is pushed out of a nozzle onto the paper. When the bubble "pops" (collapses), a vacuum is created. This pulls more ink into the print head from the cartridge. A typical bubble jet print head has 300 or 600 tiny nozzles, and all of them can fire a droplet simultaneously. Click the button to see how a thermal bubble inkjet printer works.

So that's the part that would be hard to manufacture, and even if you were able to do it and open source it, it would likely be slower and less precise than the other big companies.

I'm not an engineer, but I work tech support for one of the inkjet printer companies and we learned how the printers work. It's pretty interesting, and there's more to consider than you might think. Like color accuracy, if you want to make green on paper then you use cyan and yellow ink. Not only do you have to worry about making sure the print head spits out the correct ratio of cyan to yellow, you have to worry about which color it deposits first. If it drops yellow first, that's going to be a slightly different hue than if it deposits cyan first. So how do you make sure it deposits the correct color when the print head is moving left to right and back to left? If it deposited ink on the return back to the left, it would be dropping the opposite color first so your colors would be slightly different leading to visible bands or lines. And having the print head return to the left side without printing would take twice as long to print. You have to design the print head with that in mind, and more.

Anyways, I'm sure it's possible but it would take a lot of time and effort to make sure it worked well enough to be comparable to the big names with proprietary tech.