I'm not in the habit of giving big overarching labels of "good or bad" to stuff like this. All character design details, all archetypes, all story concepts, etc., all of these things work when approached with a (skilled) eye at making things work. Even totally stereotypical characters, or characters from archetypes that are basically loathed (like mary-sues) are beloved when handled right.
If a scarred character seems over the top, perhaps it wasn't the right detail for that character, seems off-kilter from other elements of the character or story, or maybe the story isn't over-the-top enough, or address the scar thing in the proper way.
In general I like wounded badasses, so I like scarred characters a little more than some other archetypes maybe, but I've seen bad ones and good ones. I don't think a physical feature is a good example of something that can make or break a character though.