I'm not sure you can run with appropriate gait (stop heel striking) in modern mass market running shoes. The heels on many running shoes are 2 inches+ and make it just impossible to avoid heel striking without wasting a lot of motion picking your knees up.
Also, the chances of twisting your ankle when your heels are elevated that much from the road is far higher as well.
Also, the chances of twisting your ankle when your heels are elevated that much from the road is far higher as well.