While I agree with a lot of what you’ve said, I take issue with this point:
A suicidal person is going to wind up dead, gun or not
I work with a lot of suicide survivors and I can tell you for a fact that a lot of people (I’d argue the vast majority) who attempt suicide but survive are not guaranteed to die by suicide later. Oftentimes an attempted suicide is in reaction to an event or circumstances, and once those are resolved the suicidality abates. Removing guns from the equation reduces the chances of completing a suicide, and therefore increases the chances of a suicidal person receiving the mental health care they need after an attempt.