Toucannon use their huge beaks to communicate. If you see two of them smacking their beaks together, don’t worry. They’re not fighting—they’re just telling each other how they feel.
-New Pokémon Snap
This Pokédex entry seems to imply that their angry exterior is either misunderstood or just for show.
Toucannon are actually depicted as compassionate Pokémon:
Known for forming harmonious couples, this Pokémon is brought to wedding ceremonies as a good luck charm.
-Ultra Moon
Pairs of Toucannon are considered symbols of companionship, as these Pokémon will raise the temperature of their beaks to warm each other.
-Violet
It's true as well that when they heat their beaks, it adds to the angry facade. However, I don't think people would bring them to their weddings if they were actually angry. It might be a show to intimidate predators from approaching. Or, more likely, Toucannon just have a unique way of impressing/communicating with each other.
However, it is most certainly a signature aspect of their design:

(Perhaps he was inspired by Angry Birds?)