Well, in my state, you don't "apply" for a gun like you apply for a license. It is just document that you purchased it after the seller runs a background check.
The government isn't attesting to your capabilities - that is still on you as a citizen.
But that's an outlier. In normal countries you apply for a license, THEN after you get it, you're allowed to purchase a firearm.
> you don't "apply" for a gun like you apply for a license.
>... background check
Who requires these background checks? Because the seller wouldn't do them unless obligated. Obviously the check and paperwork around it constitutes at least a de facto application to the government for permission to purchase the firearm.