Was... was that nonsense supposed to be some kind of "gotcha"?
Giving the federal government the option to deputize individuals as international agents does not even remotely suggest that States were agreeing to completely abolish all their local gun-laws for all time.
That's like claiming the permission to establish a national postal service somehow bars States from having DUI laws, because any drunkard could maybe suddenly be hired as a postman.
I believe the argument is that in order to have the Letters of Marque be useful, it must have been the case that captains had these types of weapons.
So, to fit it into your analogy, I think it is more like the permission to establish a national postal service implies that the government in the past had not outlawed literacy. There is no need for the government to provide services where the only possible users are already breaking the law.
That said I’m not actually sure I believe this because ships have always been a bit weird legally, going about in international waters far away from any law enforcement… it wouldn’t surprise me if there was some specific cut out for weapons that were only to be used at sea or something…
The point is that they implicitly expect private entities/individuals to be able to own and deploy "go toe to toe with the the state equivilent" quality units (though I don't think they expected the same quantity at that quality).