The problem is you are assuming a robbery is just a robbery, that cooperation ensures the victim's safety.
Plenty of people have gotten hurt because the robber thought the victim was holding out. People also get killed because the robber's mask fell off or they were otherwise recognized. Or just because the robber was jumpy because he needs his next fix.
You're assuming the bad guy can continually point his gun at his hostage.
In my own home, having a gun at all is a dangerous proposition: it would make my home a target of robbery if my gun ownership became popular knowledge, it would make me and my husband categorically less safe FROM EACH OTHER, and it wouldn't stop an armed robber in the house; there are no good sight lines or cover positions in my home. Again, my best shot would be to acquire an appropriate melee weapon and set up an ambush.
You're looking at using a gun offensively against an intruder. The much more sensible course of action is to choose an ambush position from which you can defend all the people in the house. Clearing the house is not the job for an individual unless they have no choice.
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Exactly. Because a gun isn't useful in every situation, it isn't useful in any situation.
Would you also agree with inverse argument? "Because a gun is useful in some situations, a gun is useful in every situation."
Of course not. If it's not useful then don't draw it.