Thank you for the feedback, these are good suggestions. The initial idea certainly was to have some dice have special abilities. We wanted the mana dice to also have elements that would create different effects for different actions, but this did not make it to the final scope.
However, even in the current version, there are multiple reasons why not to use the highest rolls available. For example, you could have rolled 8 on d20 and 7 on d8, so you use the d8 to save the d20 to the next turn. Or you only rolled defense and you are able to get enough defense with smaller dice to save the big ones for the next turn. Finally, you could roll only attacks so you know some of your dice will die and the ones assigned to heroes die first so by not using the strong ones you are again saving them for the next turn.
The strategy has probably not been so important because we made the game intentionally very easy so if you don't skip levels you can win all combats with ease.