Are there any games that actually use $2001 D0?
Most certainly!
Super Mario Bros 3 uses the grayscale bit when you complete a fortress level (to flash the screen gray several times).
Final Fantasy 1 uses an interesting cycle-timed trick using grayscale to make a diagonal beam of light when you use a particular item.
There are probably plenty of others I don't know about...
Dragon Warrior 2 (maybe some of the other Dragon Warrior games as well) uses it to flash the screen when a monster encounter occurs.
An interesting one that I know of is Noah's Ark (E), where the water effect is made by using a combination of colour emphasis and monochrome.