The Rambam said in his Mishneh Torah that it's sometimes useful to act angry:
If one desires to instill reverence in his children and his household, or in public if he is the head of a community, and he wishes to show them his anger so as to bring them back to the good way, he should only act angry in their presence so as to reprove them, but within himself he must remain calm. He should act the part of an angry man, when in reality he is not angry. [Hilkhot Deot 2:3]
So, was Moses' breaking of the tablets just an act?
The Rambam notes that when the people complained of lack of water and Moses responded:
Listen, you rebels, shall we get water for you out of this rock? [Num. 20:10]
Moses was really angry and it was not justifiable, because not all of them had been rebels in the Korach rebellion and all were suffering from thirst. So God did not forgive him. [Rambam, Shemoneh Perakim 4]
But we know that God quickly approved when Moses broke the tablets seemingly in anger. Why? Could it be because God knew the anger was not real, only staged? Is this discussed anywhere?