This is a very superficial statement. Not all cells are renewed and not everywhere. And even if they are renewed, like the skin, then they must come from somewhere, in this case from the basal layer of the epithelium, which is destroyed with deep wounds. In fact, the skin as a whole is rarely completely destroyed, more often the epithelium is destroyed and the dermis and hypodermis remain. But if the basal layer of the epithelium has died and the defect is wide, then there will definitely be a scar. If the defect is insignificant in area, then it has time to overgrow before connective tissue comes in its place in the form of a scar. If he fails, the outcome is obvious.
I am not a biologist or a doctor (forgive me, if I don't answer that way, you can minus). But I see two cases: the scar does not disappear, because its cells are also renewed; and the scar disappears but sooooo slowly.
From my own experience I can confirm the second case. In childhood (it seems even before school), the boys and I loved to burn fires and throw plastic bottles there. And of course we loved to plant such a melting bottle on a stick and make the ants "meteor shower": D
Well, in general, once I got into my hand with melted plastic. Now I'm 23, and during this time the scar has become somehow less prominent and almost half-merged with the texture of the skin. That is, it really became less noticeable.