You mentioned that you can have some White and/or some Black.
HSV allows you to have any value for the H component and:
- A High V, Low S gives White
- A Low V gives black
In other words: White and Black can give you Red OR Green OR Orange OR ... etc if you only judge by the H component.
Personally I'd say stick to RGB (or BGR whatever), or compensate for the fact the S and V can affect the colour.