Paul says that we should submit to judges for good the sake of conscience. Those who take things into their own hands might end up doing the wrong thing. If we submit out situations to good judges, we can accept their decisions with a clear conscience, knowing we have done the right thing.
Therefore you must be subject, not only because of wrath but also for conscience sake (Rom 13:5 NKJV).
The word wrath also takes the meaning “abhorrence”. We submit to judges because we have an abhorrence of all crime. Christians should not just want justice in the situations where they have been mistreated; they hate injustice so much that they want justice for everyone.