I don't know of any printer or digital camera that have a counter bomb as you describe.
True may have counters to help you in some manor:
In the case of digital cameras it's no different than a films exposure counter so you know how many pics you've taken and to ID each photo by. It's possible your cameras counter may have a limit (9999 or something) but every camera I've used or seen can be reset or restarts back at one once it hits it's count limit.
As far as printers this is to tell you the milage you have as you may need to replace things as they do wear out or runout. The toner or ink often linked to the counter and the photo drum in others. It's possible once the counter has hit a point the device will stop functioning until you replace or restock something like Ink or toner. But once done the system will reset and continue to run.
Forcing the device to override its programing is not wise. I would recommend you check out the devices manual on what sundries you need to replace on your printer.
Heres the Epson ink supply web page: Epson Stylus PX710W
Heres the Canon ink & supply web page: Canon IP4500
Marc, iFixIt can't be everything ;-}
You really need to look at the product vendors pages first and don't be so paranoid (thinking Apple or others are Big Brother). I'm not saying they don't have their moments in watching us a little to much, but, their reasons are not at the level of George Orwells' book 1984.