There are some who say, "swelling is the greatest enemy of healing." Early treatment for any acute sprain or injury is to limit painful swelling that occurs with inflammation. Holding off swelling altogether or at least reducing it may also improve joint function.
There may be some research to call this assumption into question. A recent study of ankle and foot swelling early after injury showed no link between ankle swelling and ankle function. There may be some long-term benefits of limiting ankle swelling. Less swelling may mean less joint damage. Less swelling may also mean return to normal function sooner for the nearby muscles.