The Cross-body punch gets a lot of momentum by its diagonal movement from the opposite hip to the final strike, which is about shoulder high.
The key to the cross-body is the placement of the punching hand. Imagine you are drawing a sword, getting ready to brandish it in front of you (I’ve been reading the word “brandish” in the news a lot recently, so thought I’d join the bandwagon!). With the right hand, you’d draw the sword from the left side (thumb down). Lead with the elbow to the target, then the forearm and fist whips out to make the strike.
Here’s a short video below.