It tends to bother me when people thinking that the heels far down is needed while riding english. I had trainer once that punished everyone in my lessons again and again because I could not get my heels down. When I finally managed to make it look like my heels were down I was in excruciating pain and it brought back my shin splints with a vengeance because I was rolling my ankle and forcing my heels down. But my coach was happy with it because it 'looked right'. Truthfully I have very short muscles and tendons, and with multiple Track injuries I was not flexible as everyone else.
The importance (I later learned after ditching the instructor) is having your WEIGHT in your stirrups. You do not want to be pushing with your toes but more of resting and relaxing through the stirrups while using them as a support. My heels tend to be horizontal or a tiny bot below the horizontal, but that is where my physical body will let me be. I am secure and balanced in line with my ear,hip,heel perspective. What it should look like is if you put the ball of your foot on a step and let the rest of your foot and heel hang over and relax, whatever position your ankle takes is one similar to the look in the saddle.
An exercise to show you why having you weight in your heels is important is sit on the back of a horse, let your heels be up and have someone pull your reins forward towards the horses head, mimicking if the horse threw its head or put it down to buck. You will find yourself on your horses neck and there is little you can do about it. Then put your weight in your heels and have the person pull, you will find that you have better balance and security to hold yourself up in that instance.