Local government officials said they didn't "feel safe" with the new law, even though by virtue of being an unsecured building, nothing prevented a person with illegal intentions from entering with a weapon before or after the law. The law just exposed the faulty thinking that a "no guns" sticker on the front door would keep bad guys out.
We buy expensive wines over better cheaper ones for the sake of feeling better. It's a life of interpreted experience not cold logic. Life would be too complicated to think of the actuality of everything.
It's got commonality with say a concept like pervasive direct democracy. Imagine having to make a decision a d vote on every single government act., even if only local. Most people would become exhausted of the process of this indefinite mobilization mindset.
So feeling more secure is easier than actually being statistically more secure. Peace of mind is important.
Look at insurance. You could probably run numbers and find other ways to minimize loss in the event of something catastrophic, but most of us just buy into external public insurance policies.