The American obsession with guns goes deep, all the way to the very conception of being American. The country was founded on a settler colonial fantasy of exploring a new (to Europe) frontier, and the actual settlers had to be quite self-reliant, often living in very remote areas in challenging climes. On top of the settler-colonialism, there grew a strong identity of self reliance and rejection/independence of society. I think some early American settlers were really self-reliant, having acquired their own means of production and in fact not needing to interact much with society. Of course, the majority of Americans were urbanites from the beginning. Yet, the idea of the frontier was always prominently in mind and cited proudly by all Americans regardless of their actual lifestyle.

I will gloss over a lot of American history and simply state that augmenting the national military with state militias made sense both before and after the American Revolution, so it is not surprising that a limit was put in place (the 2nd amendment) to prevent the federal government from monopolizing access to guns. But this was in large part a consideration of the rights of state governments vis-a-vis the federal government, in terms of their own established militias which already existed, not necessarily for random joes to open-carry in their local Walmart.

That is some historical context for the early link between gun ownership and American patriotism ... the question remains, why has it stuck around even to the modern day, when the vast majority of Americans were born here and live in urban cities far away from any "frontier"?

I think that question is the one most people, especially non-Americans focus on. Clearly it is the result of a concerted propaganda effort on the part of the US military/Hollywood, and in recent decades, the Republican Party and NRA. They have morphed the existing frontier mindset into something somewhat new and more abstract, a generic anti-authoritarianism in which the gun owner no longer defends against a specific foe like nature or "savages" or the British, but organized society in general, which they blame for eliminating the Wild West which they so desperately wish still existed in order to live out their settler-colonial fantasy. (See also: Westworld)

Didn't expect to write this much, but my point is basically that it will take a lot more than solving material conditions of poverty to eliminate the backward gun culture in America. Like @Tankiedesantski@hexbear.net said, it'll take a concerted re-education effort to undo decades or centuries of propaganda about American culture itself and what it is to be American.