Some ink is used for servicing (to keep the nozzles from clogging), and also color ink will be used for printing graphics (even grayscale graphics). Color ink is also used exclusively to print if photo paper is selected.
HP and other printer manufacturers have different printer technologies for different needs. For inkjet printers:
Some have printheads built into the ink cartridges. These printers can typically print with one or more of the colors completely empty, or even with color or black (but not both) cartridges removed. The Officejet 8040a is an example.
Other printers have separate ink supplies and replaceable printheads. An example would be the Officejet Pro 8600. The printhead in these printers can be replaced if they are damaged by running the printhead with colors out. Some of these printers will allow printing with a color out, other will not. If the printer is run without ink in one or more colors the printer may be damaged, but the user may be able to recover without having to send the printer for service.
Other printers have permanent printheads. To run these without some ink in all the colors would risk causing damage to the printhead due to clogs, air ingested in the printhead or burned out printhead firing resistors. The Officejet 7612 is an example of this type of printer. For printers with fixed printheads this could require service to get the printer to print properly again when the ink is finally replaced.
If you never print in color a laser printer would likely be a better choice. If you occasionally print color but mostly black an IPH printer like those in the first category above may be a good choice.