I understand and agree with the rest of your point (even if you're needlessly and insultingly calling me "ideological" when I think my desires are entirely practical ones). But that's still not the same thing as saying that "there is no solution" or that the problem is "unsolvable". Doing that is making an excuse.
If you are willing to tolerate people being hurt and killed by stray gunfire, then just admit that you are willing to tolerate it and unwilling to see it solved.
This is implicitly baked into the 2nd-amendment cause. It's the primary reason this is such a hot-button political issue.
Nothing comes for free. Every benefit has a cost. In the case of guns some part of the population belive (strongly) that the benefits outweigh the costs. The rest (strongly) believe the opposite.
The benefit of gun ownership is the idea that the citizenry can overthrow a future hypothetical tyrannical government [1]. The cost is the many lives lost in the real world now.
While it may be impossible to say, the phrase "if a few children must die to protect our way-of-life, then that's a price worth paying" springs to mind.
[1] the actual efficacy of such a resistance may be questionable (it didn't help the confederacy for example) that's not really the point. The argument is that merely the threat of such an uprising prevents the tyrannical govt from forming in the first place.
Of course the argument may be nonsense. New Zealand has survived tyrany with little to no gun ownership, whereas tyrany in places with high ownership, like say Iraq, is not uncommon - which suggests there are other factors in play.
But the quality of the argument is not material. The fact is that a significant number of people believe that guns are important, and that the cost of guns is worth paying.
Ultimately that is the problem that is "not solvable".
Don't get me wrong, there have been cases where armed revolution has been successful, but in most cases, it's been average people getting out into the streets and saying enough that has made the big difference.
There are not many governments that can continue when the majority of the people are actively protesting against it.
More importantly, women in the US are literally dying due to tyrannical oppression from their government. Where are the people with guns to fight said government?
Like, if you think it's trivially solvable then just solve it trivially and we can all move on.
The practical problem is that despite risks, people choose to be stupid. I think even an uneducated person knows that a bullet fired into the air will eventually return to the ground.
The social reality is that humans oddly seem obsessed with doing things which are clearly detrimental to themselves or others, in the short or long term. This part of the problem is not at all trivial to solve (I doubt it can be solved).