Too much swelling is bad. Not enough swelling is bad. The challenge is in figuring out how much is right, and then attaining that goal.
The body’s defenses have a tendency to over-react. Often, the immune response to a significant infection can be so over-the-top that the patient dies of the defenses, not the infection. With injuries, the body rushes many factors to the site which can cause similar problems locally.
If one elevates the injured area higher than their heart, uses an elastic wrap firmly but not too tight, keeps ice on it no more than 20 minutes out of every hour, and takes some tylenol, one will be more likely to achieve a happy medium between too much swelling and not enough swelling.