However, when you try to buy more ink, you find that a black+tricolour cartridge set costs more than the printer did in the first place!
This is the well-established 'Razor and blades' tactic - you sell the razor at a loss but make a regular income from selling the blades.
To top it all, the firmware in my old printer does all it can to ensure that you only use 'compatible' (HP) ink cartridge replacements. However, in 2017 the Supreme Court in the USA (Impression products Ink Inc. v. Lexmark) frowned upon this practise. Since that court case, some manufacturers now provide firmware updates to 'unblock' their printers and more recent printers don't usually block refilled cartridges.