As mentioned, printers of all brands come with very little ink in a new printer.
If the Black runs out first, very likely indeed, then some printers won't print and some will. For those that do continue, they use the three colours to produce black and that will exhaust the three colours much quicker. For many this will have the effect of all three colour cartridges running out around the same time.
I used to use Epson inkjet printers almost exclusively then on to Cannon as they were early adopters of the multi (4) individual cartridges, not 1 black and 1 colour cartridge. At one point I needed an A3 printer and that was pretty expensive at the time, when a new OS came out 'XP' (ha, ha, new OS) I needed a new printer driver for XP and HP said they weren't going to produce one, a still working and expensive A3 printer redundant. From that point and to this day I haven't purchased 'anything' from HP.
The next scam was the introduction of chips in the cartridges to check that you were using proprietary ink cartridges in your printer to stop you buying third party ink cartridges. But then the 3rd party cartridges were able to use chips in their cartridges.
My current inkjet printer is an Epson Stylus Office BX635FWD Printer, Copier, Scanner and Fax. It is a good printer and I have been using 3rd party ink cartridges almost exclusively from when the original cartridges ran out. On occasion one of the 3rd party printers just don't want to play, not recognised by the printer, but that isn't very often.
So as you can see there are plenty of rip-offs to go around.