In the most frequent circumstance - my 3 year old hitting his 1 year old sister - my first step is to pick her up, give her sympathetic attention, and whisk her out of the room. So safety is no longer an issue, and the hitter has a moment to cool off, which they typically need. More importantly, he's feeling attention drain out of the room - while undramatic, this is enormously impactful. In the psychological conditioning literature, this is called "extinction" - you're taking away the stimulus that he's been looking for.

I'm sure there are circumstances where there's not much choice but to step in, but think hard and creatively about ways to mitigate the safety issue while removing attention. We're so driven to step in and make a scene that this is often painfully difficult.