Ink delivery is likely the main challenge (although I've seen some low-res attempts), combined with the speed and precision needed for a good printer - reaching a few hundred DPI requires positioning things quite precisely. Laser printers are interesting, but then you need specialized parts like the drum that I'd expect to be difficult to produce in single quantities.
Open pen plotters are a thing, but again not typically used for normal printing duties.
Something pen-plotters don't do (they typically want paper to be placed down for them, or work of a roll of paper), and the maybe 3D-printer equivalent of preparing the print bed and removing prints from it is a well-known source of problems and manual work.
There's a massive growth curve too. If we could find a way to print on plastic, we could integrate this with a 3d printer and make decorated parts. I think this would be multiple stages of amateur R&D, but it would eventually happen (yes, I suspect someone will respond with all the technical issues why it can't work with current technology, ignoring all disclaimers -- I am aware this won't work right now).
I think of tons of other use cases.
I think the problem is as others have described. Making a printhead costs peanuts, but engineering one and NREs are astronomical. Ditto for paper handling, and many other parts of the printer. There used to be an printhead open enough for DIY (you could buy them in quantities of 1, and there was a spec sheet), but it's not sold anymore.
You'd never run out of toner at least.
Edit, answered at least one question: yes engravers do 500 dpi routinely. Here's one: https://www.troteclaser.com/en-us/knowledge/tips-for-laser-u...
Those kinds of printers already exist commercially. The argument is the same: Printing on clothes or PCBs might be cool, but crappy DIY printers that can do that are even more niche than crappy DIY printers that print on paper.
Also, high power lasers are consumables.
Then how about a printer that can print on a large wall? E.g. with spray paint.
Nobody would accept a 2D printer that took manual intervention every sheet.
If I'm labeling pins and parts on a PCB, I'll take low-quality labels over no labels any day. If I'm labeling how wood fits together on a laser cut, I'll take it. If I'm making educational resources, quality almost doesn't matter.
If I could have a 1980-era printhead I could control, I could do a lot with it.
And if we had that, quality would improve with time. Look how many years it took 3d printers to be useful for anything practical. I expect if we started even with 1980-era inkjet quality, we'd get to nice in 5-10 years.