Part of this is a lack of understanding that the low point of the swing is on the target side of the ball.

I think this is a great question. Part of this is a lack of understanding that the low point of the swing is on the target side of the ball. From the outside it can appear that golf is a “lifting game” that you are trying to help/lift the ball up in the air. Because of this people tend to hang back on their trail leg in an effort to lift the ball off of the ground.

One of the first things people need to learn is how to use their lower bodies, especially on the forward swing. I believe in making the swing athletic, getting them to understand that swinging the club has similar aspects to throwing a ball. The lower body has to lead the forward swing. I like to have them throw me a medicine ball (6 lbs) in the same concept of a golf swing. This is a big eye opener for them.
I also like to put a spot on the ground an inch or two on the target side of where the ball would be and have them try to strike the ground on that spot. After a few successful practice swings we put a ball down and have them try to strike the ball and then the spot on the ground. This is a great non-technical way to get people to let their lower bodies lead the forward swing and then to learn proper ball then turf contact.