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.
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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?
RepRap printers have existed for a while
I can't think of any reason, exactly. FairPrinter could exist, somebody just has to make it.
I found this: https://hackaday.io/project/167446-diy-inkjet-printer
That's just a 3d printer with extra steps