Much of Saturn's current time is spent researching, exploring and promoting the arts and sciences and leading his nations scientific and cultural development. Of course mostly before the war.
However, he is still a disciplinarian and doesn't tolerate misbehavior among his staff and assistants...
Fighting without paying attentions to your surroundings is not a smart idea for a hero, as Todoroki and Bakugo learn when Aizawa interrupts their fight. Getting on the bad side of the grumpy and perpetually sleep-deprived teacher is not a good idea.
Taking a dragon to a party can be dangerous, especially when shinies abound. Remiel learns this the hard way and then Tempo learns the hard way that a game is only a game if everyone knows they are playing.