3. The 1-shot Cop is useless. If Joseph is indeed town, then maybe scum will kill him tonight to prevent an investigation. What's much more likely though is that they will simply roleblock him. In that case we don't get any information, and our Cop shot goes to waste. Much better to give the shot to the unknown UB, who has in fact a chance of actually catching scum with it.
How do you know there's a roleblocker?
You don't, unless you're scum, it's perfectly possible that the mafia could be normal goons.
The chance of 6 Ts is 1/64, the chance of exactly 5 Ts is 6/64, so there's a 7/64 = 11% chance that there's no roleblocker (please correct if maths is wrong!). In that case, lynching me seems really bad, as it gives all the killing power to the scum team.
Plus, there's no guarantee that I will use the shot, so if you don't lynch me, I could always
not use it, and so if I die, it passes to the UB anyway. Adding uncertainties for who the scum should kill can only be a good idea IMO.
Back to Joseph for a minute:
Yes, but the case is bad because I can still use my cop ability, and the fact that the scum won't know if I'm using it or not posess problems for them- to kill me or not to kill me? If there is a roleblocker, then my presence may cause them to waste their ability on blocking me, and not another PR (it's likely there is another PR in this game), which is good for us. If there's a doctor then this case is terrible, since the Doctor can save me, which means there probably won't be a NK, plus I get to use the cop ability.
Granted, the doctor can't protect who they want, but I'm probably the most likely target anyway, so the one who needs protecting.
faust's case seems strong if and only if the mafia have a roleblocker
and we don't have a doctor to protect me. But this isn't guaranteed, and if this is not the case, then I believe that the above shows I'm still useful to town.