Oh! One thing to note, I have found that the chilli powder over here is not the same as in North America. The stuff I've been able to get here has been plain ground chillis rather than what Americans know as chilli powder. The stuff we got back home has ground chillis, oregano and cumin which gives it more of that 'Mexican' taste.
In the past, we've had people complain on the forum previously about exactly the opposite - that the chili powder here has too many added ingredients, compared to in the US - lol!

I think it depends on where you buy your chili powder & which chili powder product it is - just important to check the label before you buy, so you know exactly what you're getting in that particular chili powder.
For example, Sainsburys Hot Chilli Powder contains: Cayenne Pepper, Paprika, Cumin, Oregano, and Garlic. Whereas Sainsburys Mild Chilli Powder contains: Chilli Pepper, Cumin, Oregano, Garlic. Schwartz Hot Chilli Powder: Chilli Powder (Chilli Pepper, Cumin, Salt, Oregano, Garlic, Anti-Caking Agent (Silicon Dioxide)), Cayenne Pepper (20%). There are others that are pure plain ground chilies, as you have indicated.