Theoretically: no.
In practice, in the world we’re living in? Hell no.
Any attempt to prosecute the killer would simply add to the advantage the ruling class already have, and be basically an injustice by definition no matter how “by the book” could it have been approached in the otherwise wondrful and illusory world of theory.
I wouldn’t say it’d be “in their favor”. To be honest, I don’t think even the ruling class has a way to make this smply “go away” in the “make sure polices and judges do not pursue this case” sense, and even if they did that’d just spark more animosity towards them that they have this power (i mean, we know they do, it’s just now it’d be visible) and they’re using it.