You also have a right to travel around the country, but that doesn't mean you're allowed to drink and drive. There are plenty of valid, constitutional reasons for firearm ownership to be restricted to qualified individuals. When these restrictions are in place, many fewer people die. It is what it is.
Also, what a shitty analogy: suicide is by definition a self-harmful act, DUI is almost always a socially-harmful act on its own.
(And in many states, you can DUI on private property, by the way.)
"59% of people who died in crashes involving alcohol-impaired drivers in 2022 were the alcohol-impaired drivers themselves"[1]
Also, people who commit suicide with their firearms typically have families who suffer.