If we assume that the balance should be weighted in this way, it is because the consequences for the people involved are much more important than the loss that will be suffered by the public.
We need the press to have freedom so that we can remain informed about what is going on in our society. If we do not remain informed, we cannot be good citizens because we cannot properly know what to demand from our government. But protecting the privacy of people in a criminal investigation does not take much away from our ability to get the knowledge we need. We do not really need to know all the details about such investigations before they reach trial.
By contrast, the people involved really can be hurt by the publicity. If their names are exposed in the press, they can have their lives destroyed even if it eventually turns out that they are not even charged with any wrongdoing. Therefore, the harm in allowing the media free rein outdoes the harm caused by reducing the media’s right to report on criminal investigations.