As it says in https://en.wikipedia.org/wiki/Philip_Hamilton "For the first minute, both men stood, doing nothing, both refusing to shoot." It seems they weren't really that adamant about killing each other.

It's also argued that Alexander Hamilton threw away his first shot when dueling Aaron Burr.

It seems duels were well planned in advance. If people preferred to deescalate the situation, why wouldn't they just decide not to duel in the first place? A duel requires two willing participants.