Is there a better way to explain why $\phi \left ( p^k \right ) = p^k - p^{k-1}$?

I think your explanation is the simplest. Here's another way to look at it that may provide a different kind of intuition. Factor out $p^k$ to get $$ \phi(p^k) = p^k \left( 1 - \frac{1}{p} \right) $$ which tells you to throw out the fraction of the numbers less than $p^k$ that are divisible by $p$.