First off, besides deputies, P.O's weapon is not a long range weapon, so there is no sniper shot for them, because of inaccuracy. So, using a closer range weapon, for a sniper shot is a bad idea. The next step up, in terms of weapon range, is the corporal gun, and if there is a corporal playing, he should be the one doing the negotiation. Same thing with a higher rank than corporal, and so on.
Second, officers never purposely fail the negotiations.... They always try and work with the hostage taker to keep them calm and let them know you are trying to do something to help them. This also includes stalling them, and telling them they are getting something the hostage taker wants, even though the officer knows that can't happen.
Quote: "Taking down criminals is the job of the police department. " - To a certain degree, yes. But, another main objective is to maximize safety and minimize casualties. Also, cops do not purposely fail negotiations to kill the bad guy. The objective is to always get the hostage out safe, and the bad guy detained....alive.
I understand what you are saying, and your point, but you are the one looking at it one sided. The reasons we have negotiations is to come to a common ground, on a decision. If that can't happen, under certain circumstances, then an alternative solution has to happen. Purposely failing negotiations is not RP-ing it at all; its "wanting" to kill the hostage taker just because you can. Of course your previous situation can work, but taking down (killing) criminals is not the police's job, it is to save the good guys, and detain the bad guys, and that doesn't mean kill them in every hostage situation. I hope the other side of the bridge makes sense to you.