I think you can give SK substantial extra powers and still not overbalance the game. My Trifia game had a mechanism by which players giving incorrect trivia answers were denied their night choices. My SK was immune to this. The SK was also immune to investigation by a variety of non-cop investigative roles; only the standard cop would get a guilty result. The SK's kills were also doc-proof; a doctor protection of a SK target would not save their life.
Despite this, the SK was cop-investigated several days in and lynched. Had that not happened, I think the player probably would have been night-killed shortly thereafter.
My general stance is that any role that
must
survive until the end of the game to win (SK and certain types of neutrals, generally) deserves all the help you can give them. There are too many ways that sheer chance can result in their death, even given the very best possible play on their part.
It takes a village to raise a lynch mob.