These 8/16bit cores are rarely used for the main function of the device. They often exist as a general purpose controller to glue together random logic. For example, they might implement the logic that makes the LED be blue when the device is on, and flash blue when the power button is held for 3 seconds, and then trigger a power off when held for 10 seconds (or whatever).

They sometimes might even exist along side of a fully 32bit ARM micro.