The biggest problem I see is cop going to somebody who can manipulate it due to bad luck, so if we're worried about that we can swap Shadoweh with somebody who looks really townie by the end of the phase. I guess.
I have thought of a potential scum counter but there's also a workaround on town's side. If we go through with the plan, I won't disclose this until we've already picked, in case scum doesn't think of it.
@Dormio: imo it's better as is because this way, the cop can get results out ASAP, the tracker stops a scum rolecop from hunting for the doc (unless they're buddies), and the roleblocker is held 100% accountable to make sure they're not blocking the doc/cop.