If I had those long nape trails (or side burns for that matter lol) Id probably clean it up. I don't like that look, so it's a personal thing. My nape line is neat-ish naturally.
I edge up, but not into a rounded or straight shape.
I actually make a look natural by creating a sloppy W shape, so some parts of the nape start a bit higher then the other parts. My hair is all down my neck, so I have to stay on top of it.