If a player gets hit in the throat and collapses his airway, stopping play and getting him help 10 seconds earlier is not going to matter. This is a situation that requires trained medical personel and unless they're sitting outside the gate, those extra 10 seconds won't help.
The same goes for lost eyeballs, missing teeth, punctured lungs, or any other horror story you can dream up. Most of these medical emergencies require medical personel that simply aren't present. The 10 seconds it takes for you to kill the play is only a small portion of the 10 minutes it's going to take for the ambulance to arrive.
We can make up "what if's" all day long if you'd like, but what's the point?
Again, I think an appropriate guideline to use is, "would I grant time if asked?" If you would, it's probably an acceptable time to kill the play.
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