Injuries can happen if your snake isn't hungry enough to hunt the prey right away, or if it tries to kill the prey but doesn't have full control over the prey or is unsuccessful with its strike.
Additionally, feeding killed prey allows you to buy frozen prey items and stockpile them in the freezer so it is easier to have the proper sized prey on hand at all times. Running out to the pet store for food every time your snake needs to eat or raising your own prey can also be more expensive and time consuming, and doesn't guarantee you will be able to get the right sized prey at the right time. Some pet stores will sell frozen prey or fresh killed prey which you can then freeze for later.
Most snakes take fairly well to prekilled prey, although it is best if they have been accustomed to pre-killed prey at a young age. If your snake is eating live prey, you may need to start out offering freshly killed prey at first. Frozen prey should be completely thawed and warmed slightly before feeding (defrost in the fridge or in cold water, not at room temperature, then warm slightly in warm water just before feeding). Dangling the killed prey and wiggling it a bit with tongs (never hold prey with your fingers) can help entice a snake to take the prey. If your snake is still reluctant to eat, you can try dipping the prey in chicken broth, or pithing the prey (puncturing the skull to expose the brain).