The manufacturers ensure that their warranties include some such as "...only original carts should be used..." - these days, you can buy a halfway-decent printer for the cost of a set of original inks - use up the ink supplied, buy compatible carts, if they knacker the printer (doubtful), buy a new one.
I buy compatible cartridges for around £1 each - on my current Epson SX435W, only one has failed in over a year. I use the same supplier on eBay & have been very pleased.
By the way, when the carts that came with the printer run out, keep them! If compatible carts should stop the printer from working, you can replace them with the originals & say "Duh!"
IMO, of course - I'm not suggesting anything underhand.
No, really, I'm not.
Honestly.