Just because something heals doesn't mean there isn't a scar. If the wound is deep enough, there will certainly be a scar; it doesn't "go away" like that. But that doesn't mean the wound has not healed.
Look at it this way. A physical wound that's serious and deep enough to leave a scar is generally incapacitating, at least in the short term. The same can be said for emotional damage, too; most victims of severe emotional trauma exhibit very pronounced symptoms related to the trauma for some time. But except in the most extreme of cases, both types of damage will, after a time and proper treatment if necessary, cease to be incapacitating. This is the critical point.
Maybe a scar will be left. It may even flare up on occasion; this may or may not always even be a bad thing (just as some people can sometimes sense changes in weather by the way old scars flare up, so can the unexpected flaring of an emotional scar be predictive of a potential bad situation). Perhaps it is not complete healing in the sense that a paper cut heals over until you can't even detect that it was ever there, but one can't deny that it's still a kind of healing.
Complete emotional healing does exist for minor wounds, just as for physical ones. I'd imagine all of us have had someone be rude to us in the past. Most people encounter rudeness every day in some form or another, and the result is generally bruised feelings. But do you remember every single occurrence of this? Probably not; the hurt from these has completely healed over. But remember the nature of this: just as complete physical healing leaves no mark whatsoever, complete emotional healing leaves no mark on the mind; in other words it is forgotten.
Given that, would people truly want complete emotional healing for major events? The only way for that to happen would be to completely forget whatever experience caused it, and depending on the trauma one may need to forget everything related to the it (such as completely forgetting a lost loved one). In the end, that would be the true loss. Remember, broken bones come back stronger, even though they are scarred. The same can be true for emotional damage.