America has an unusually high rate of suicide. When we consider that most suicide is more "opportunistic" rather than planned, and that guns are hands down highest scoring across quick, painless and irrevocable, it's not unreasonable to consider the people who only successfully attempt to kill themselves because of access to guns when we consider the specifics and legality of access to guns. We can't attach an exact number to that, but it's safe to assume from what we do know that guns play some part in a significant percentage of suicides.
>unusually high suicide rate
That is a claim about facts which in turn you use to build a whole narrative, lets see if facts agree in the first place.
en.wikipedia.org
www.macrotrends.net
That's 4 sources using different years and data.
Conclusion: No, US suicide rates are around upper end of the average when compared to the world in general. USA has nothing on South Korea for example, and that's a similarly developed country with extremely low gun ownership rate.
USA is not far off countries, from more notable and developed ones, like Slovenia, Estonia, Belgium and Sweden, none of them famous for high gun ownership.
Switzerland is famous for being one of very few US peers in at gun ownership among wealthy countries, but in suicide rates, while many spots lower, in raw number rate is about 30% lower than USA, and in turn pretty average by Europe's standards.
And nothing besides perhaps terrible stat keeping explains the suicide rates of third world countries with guns sold in open air markets to whoever can pay if we were to take your theory seriously.
To me it seems there are different factors that should be looked at to explain it at national scale:
>don't be a vodka abusing post communist mess, or a communist mess in general
>don't have a high pressure work culture
>don't have weird cultural factors
>have nice, comfy weather year round
>have highly religious population
If you even think of limiting suicide by controlling the access to means, then alongside guns you would also need to cut access to the other obvious ones, like cars, tall buildings, sharp objects and household chemicals. Or in other words, put that person in a padded cell already. And its really unfeasible to turn the whole country into that.
And if we look at USA with more resolution, you get this:
If guns are a meaningful factor, then why do the southern states famous for incredibly high gun ownership, like Texas, have average or below average suicide rates?
Who's really pushing up US suicide rates is the west, California excepted (could be its infamously high immigration from countries to the south that according to maps above have low suicide rates), and at the moment i have no idea what's so wrong with them.