Have you ever considered that the gun policy in the U.S. hasn't failed, but rather it's a failure on the part of psychologists and psychiatrists? Perhaps their methods for determining who is suitable to own a gun are inadequate, or maybe they allow clearly unstable individuals to remain free.
This is, admittedly, an extreme point of view. In reality, it's likely impossible to perfectly assess someone's mental fitness, and perhaps efforts should focus on stopping black market sellers and improving mental health evaluations.
However, even with these measures, the presence of lethal weapons can always lead to negative outcomes. For instance, a gun owner might have a troubled child who gains access to the firearm and causes a disaster, or someone might act irrationally during a panic attack. Additionally, accidents can occur due to negligence, or firearms might be stolen and used for criminal purposes.
With all that being said, wherever weapons and guns are present, tragic events can always happen, regardless of policies, mental health checks, or other factors. In today's society, disarming the population takes away the right to self-defense. Completely disarming everyone is difficult but might be possible. If not, whether we maintain the current situation or tighten or loosen regulations, I think things will continue the same.