Standard disclaimer: I’m not an expert, sniper, or hostage negotiator, nor even a policeman. Rather, I’m just a dude who’s pretty proficient with guns.
I think that trying to shoot the bad guy while he was holding a gun to a hostage would not be good tactics. There are a couple of reasons for this:
As the OP mentions, if the muscles contracted with the hit, you’d lose the hostage. I haven’t been to medical school so I can’t say whether or not this is a common phenomenon, but I certainly wouldn’t rule it out; nor would I want to be the guy that had to provide the test case.
However, an even bigger concern (for me, anyway) is that headshots aren’t always lethal. I don’t think it’s a stretch to say that the round could, say, fragment on a skull bone and, rather than penetrating into the brain, would simply “skip” around the skull - maybe inside the scalp, maybe not.
Plus, your average policeman/law enforcement officer isn’t nearly as skilled at shooting as the guys in the movies. I’ve shot the Texas DPS qualification set, and it’s almost ridiculously easy to pass. I have a buddy who had only shot a handgun once before, and was half-blind in one eye, that was able to pass the test, even the shots from some distance away (IIRC, it was 20 yards.) That’s not to say that they’re unskilled, by any means. And, of course, some of them shoot competitively and are remarkably good, but I’m pretty sure that your normal, everyday beat cop isn’t a superior pistol marksman.
Add to that the stress of the encounter. Lots and lots of police shootouts occur at minimal distances with no one getting hit, even after emptying magazines. Loss of fine motor control and all that.
Plus, service handguns aren’t coddled - they’re banged against doorframes and such quite a bit (I carry concealed on my right hip, and even after doing this for years I still occasionally give my pistol a good bump.) There’s always the possibility that the rear sight (which in many cases is adjustable for windage) could be off, thereby giving a false sight picture.
Where it gets stickier in my mind is when we’re talking about snipers. Say the negotiators are doing their thing, but somewhere in the background there’s a couple of guys in ghillie suits leveling a scoped .308 at the bad guy’s eye socket. I have no doubt in my mind that they would likely get their hit - they’re trained for bullet drop compensation, windage, distance, etc. The only X-factor, really, is the bad guy. If he moves at the last second, all bets are off. If someone had to take a shot at a bad guy, I’d hope it’d be a sniper rather than a beat cop with a Glock. Would it ever be given the go-ahead by the upper brass? My hunch is no.