If your gun is kept properly stored, the risk of an accidental injury is zero. If you are suicidal, you shouldn't have access to a gun, or a car, or any sharp objects, or any rope, or any medications, or any bridges or tall buildings, etc. I'm all for punishing people who don't store their guns correctly and whose kids accidentally or intentionally get ahold of them and harm themselves or someone else.
If you want to get pro-2A people to budge on gun control, do something about the people that are already illegally carrying and using guns. When seconds count the police are minutes to hours away. People realized in 2020 during the pandemic and after the riots that the government can't protect everyone all the time. At some point responsibility falls upon the individual, and taking away an individual's right to defend themselves or their family is a non-starter for many people, myself included.