They can also be useful if you want to stop paying that nearby city-state in order to get its luxury resource. Just culture bomb into the luxury reaource and you're saving yourself a good chunk of gold.
If an AI civ was allied to the City State you culture bombed for said luxury, would it affect your standing with that AI civ?
I've never used a culture bomb, since I go for science. I would rather have the golden age bonus instead.