Isn't this why some close protection details train that weird "draw and shoot from the hip as fast as possible" move?
With enough training, experience, and alertness I'm sure a gun would still be useful in a knife-fight situation. That said, getting shot doesn't always stop the attacker and if they're in conversational range then you're probably gonna get cut even if you do get shots off.
Not to mention the majority of Police and even military wouldn't train properly for this.
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