*Read: I know this because I often pick these up for nothing and use them as a cheap scanner.*
With Epson it’s almost always a hardware flaw. Epson has designed their printers so the printhead is difficult to remove for normal users - it’s not an issue if you’re used to it, but it gets first timers all of the time. At this point, clogging is a well established design flaw Epson has yet to fix because they make so much money on consumables since they change them every refresh.
The issue is usually caused by OEM Epson ink (and is compounded with false “security updates”, which only block 3rd party ink carts). Pigment is far worse then the dye ones as well, but it happens on both. The other common issue is printhead air, but that’s usually associated with inconsistent print quality issues. That can be fixed by forcing the air out. If it’s clogged, the cleaner can be found on eBay. NEVER UPDATE THE FIRMWARE ON EPSON PRINTERS! Let them live with the fact their BS “security updates” leave printers open to attack.
PS: I used to love the Epson printers for scanner use, but after the black cart bait and switch firmware I’m pretty much done with anything Epson - even used. They have some of the best scanners I’ve used, but the firmware issue makes it hard to know if it’s going to be cheap or expen$ive to put ink in if need be. Especially if I don’t know the WIC usage and waste ink pad saturation.
However, as much as I want to tear into Epson they’re no worse then HP with the dynamic security printers, which is a way to progressively block 3rd party ink over time. The difference with HP is that they DO allow you to use the printer with the original chip, while Epson straight up disables it - HP only cares in terms of the warranty for the most part. Eventually the clone chips bypass the dynamic security, but you can never update the firmware if you can absolutely avoid it. At least HP is honest unlike Epson. HP also has Cartridge Protection, which “locks” the chip to that printer so you usually need to kill that before installing the ink if at all possible or burn the first set and turn it off.
Lexmark was also guilty with the 100 series printers. They used RFID chips and forced you to replace the ink with those printers once it ran out, especially with the single use return cartridges. You could replace the chip and use them again, but Lexmark is/was very sue happy if you try and reuse a “return program” cartridge. They also made it quite a pain to do, but have since walked from the inkjet market and make the lasers with the quality and moderate DRM HP used to make. I'm happier with the modern Lexmarks more than modern HP now, ironically. Same return program games, but what a 180.
All of these inkjet printers clog, but Epson is the worst of them all. You can fix it on most Canon models as long as the head is modular (not on all models), so they get a pass (somewhat). It’s usually the low, low end CLI models with fixed heads. However, they kept it modular on the higher end ones.
On the more current 564/901 HP models, HP generally integrates the head and needs setup carts to use the printer again - and you probably no longer have them so you can no longer use it once you lose the initial calibration. You need a wide body HP 95X/96X printer (OfficeJet Pro) for a user serviceable printhead with HP today.