Epson for example has print heads with jets that will clog if the color ink runs out. To avoid this and force the users to get some ink in the machine the machine stops printing.
Some HP models like the k550, k5400 also have a replaceable printhead which surprises some to cost as much as the printer. To keep the heads from clogging every once in awhile it shoots a little ink through those heads to keep it clear and moving.
About the only hope you have here is to get a printer with black only print cartridges. The bad news is there are now so few available and none in the retail channels.
-> Now you may wonder why they force this issue. It's simple. If they didn't then owners could claim the maker should pay to get the heads de-clogged or replaced.
Hope this helps explain it.
Bob