Use or Importance of $\Rightarrow^*$ operator
It is false that $\Rightarrow^*$ " just replaces the head of the production with the head itself". $A \Rightarrow^* B$ means that the sentential form $B$ can be obtained from the sentimental form $A$ by applying any number of productions (which might be $0$ or more than $0$). 

For example if your grammar is $S \to a$, then all of the following are true  $S \Rightarrow^* S$, $S \Rightarrow^* a$, and $S \Rightarrow^+ a$, while it is false that $S \Rightarrow^+ S$.

If you are deriving strings and applying at least one production per step then both $\Rightarrow^*$ and $\Rightarrow^+$ are correct. The latter is more specific since it implies the former (but not vice-versa).