The most simple answer is that: Humans don't balance on their heels. Have a friend shove you hard enough to make you move a few feet. As you scurry to catch your balance you will notice that you bend your knees, maybe bend at the waist a little bit, drop your center of gravity and put most of your weight on the ball of your feet.
When you weight the ball of your feet then your toes, and ankles/calves can affect the forward&backward pitch of your body without too much trouble.
When you are on your heels, these muscles have less influence over your body position. Go ahead and try standing straight up normally while lifting your toes off of the ground. Your knees want to straighten and you have to use your hips, back and upper body a lot more to keep your balance.
I used to teach cheerleaders how to do stunts (like these
) and we always tell the flyer (the girl being held in the air) that if she balances on her heel then niether she, nor her base (the guy holding her up) will be able to control the stunt effectively because your upper body is too slow at making the quick, micro-adjustments necessary to maintain stability. If the girl is on the ball of her foot, then she can flex her calf muscle and adjust her ankle with ease.
Next time you're next to a cheerleader that flies in stunts, check out her legs. Even if she is skinny, she probably has some developed calf muscles.
One advantage snowboarding has is that your can bend your knees quite a bit to make up for the control that your calves lose. However, if you've ever done the wall-sit in gym class... then you are well aware that your thighs don't like that kind of constant, continuous strain. My thighs are usually less baked after a 2 mile run than 1 mile down the mountain.