Gun control can work. It might take 100 years, but it could work. Gradually reduce the number of guns in circulation, make them more expensive and harder to obtain, increase penalties for misuse. It could potentially be done.
You are right that those other things you mentioned would be very good to do. But they are all approximately the same level of impossible as gun control, i.e. they might be fixed sometime after we are all dead, if the country survives that long.
But there's no reason we shouldn't take tiny, tentative baby steps toward addressing all the issues in the meantime.
barfo