There are heels in your shoes because people rode horses. A boot heel was designed to keep the foot from slipping forward in a stirrup. Heels became fashionable because they made people look taller, and because they allowed the calf muscles to shorten and look fuller. There is absolutely no good reason for a heel in any shoe, for walking, for running or for any other sport (I’m not convinced by the reasons given for heel lift in skates and cross-country ski boots).
If you are wearing a heel, it will tend to make you land on your heel, simply because it will be closer to the ground as your foot lands. If you do land on your heel, you will need cushioning as your natural shock-absorbing musculature will not function well. Also, if you land on your heel, you will have much reduced lateral strength (I don’t want to use the word “stability” here, for reasons explained later). Your will also greatly increase any tendency to over-pronate.
Of course, having the heel contact the ground first does not necessarily mean landing on the heel. I will explain. The objective in running, as in walking, is to generate forward movement, and not to waste energy bouncing up and down. This means that the foot should reach the ground before the body’s weight falls on it. If you put the foot down in front of the body, even on the heel, there is no problem if you are not falling onto the leg – if you are instead putting the leg down so that it can take your weight when the body advances over it. If you do this, you will notice that, even if your heel makes first contact with the ground, the leg will not have to absorb the body’s weight until the ball of the foot is under the body. At this point, the weight of the body over the ball of the foot will tend to cause a reflexive extension of the leg, leading to forward propulsive force. This works very well in walking.
Here is the problem. If you land on your heel when running, the muscles engaged to absorb shock are not the same as those that will drive you forward when the leg extends. Think about jumping rope — when you jump and land on the forefoot, as the joints of the leg fold, the muscles that will move you upwards again are perfectly prepared. Now, imagine (or try it out!) landing on the heels. Not only will you absorb shock poorly, you will have difficulty transitioning to jumping. The same with running – land on your heels, and you will not extend the legs well.