Why is sugar used in low-cost homemade rockets?
the best fuel is actually sorbitol. It is a bit costlier than sugar, but still cheap. It melts easily without decomposition and can dissolve some amount of potassium nitrate. Common sugar decomposes before melting.

Paraffin has one bad habit: it quite easily vaporizes. It is bad, because it makes mixture much harder to ignite and it becomes prone to self-extinguishing because of it. Many polymers also easily decompose producing much gases. Paraffin is used in some specific formulations with more active oxidizers or as a non-fuel additive.

Black powder is actually quite common, but it has very high combustion rate and is prone to explosive combustion, so it is not recommended for beginners. It also requires ball mill to make, and constructing one is time consuming.  

Added: The main advantages of rocket candy are readily available components, simplicity of preparation (no special equipment required), stable burn and safety in comparison with many other compositions.