In fact there are many studies on this and in general they show that restricting the means of suicide does actually reduce overall suicides.
Who conducted these studies? What was their political bias? I see so much prejudice against civilian gun ownership from psychologists that I doubt they can be relied upon to let their personal feelings get in the way of their preferred research outcome.
Furthermore, here in Yorkshire our total suicide rate was 13.95 per 100,000 in 2019 [1], whereas it was 14.8 per 100,000 in 2018 in the USA (latest CDC data) [2].
Not much difference there, is there? And yet, very few people in Yorkshire commit suicide with firearms (~4%), or even have access to firearms. Hanging is the commonest method here. If someone wants to kill themselves, then without a timely mental health intervention, they will find a way. They even manage to commit suicide in maximum security prisons, so trying to restrict their access to another means of committing suicide outside prison seems rather ridiculous.
[1]
Suicides in England and Wales - Office for National Statistics (ons.gov.uk)
[2]
FastStats - Suicide and Self-Inflicted Injury (cdc.gov)
Yes, USA suicide rate is 4.3 per 100,000. My figures are actually 7.32 at 2017 rate so some what higher.
I said: 'The homicide by firearms rate in the USA was 4.3 per 100,000:
FastStats - Homicide (cdc.gov)' not the the suicide rate.
If you read the line before the section of my comment that you quoted you will see I said: 'According to the CDC, the suicide by firearms rate in the USA in 2018 was 7.5 per 100,000 people:
FastStats - Suicide and Self-Inflicted Injury (cdc.gov)' which is close to your figure for 2017.
So would these suicides used another method? Suicide rate for UK was 0.16. That is almost 500 times the US rate. Difficult to dispute the figures.
Yes, I suspect the majority of them would just use a different method. You have to bear in mind that in the USA there is no NHS and people pay through the nose for elective medical care if they have no medical insurance (or a crap policy), so many serious mental illnesses go untreated there. That's also why they have so many spree-killers. They could really lower the violent crime rate and the body count by just having a robust system of free-at-the-point-of-use healthcare.
I don't know where you're getting your figures from. The suicide rate in the UK in 2019 was 11 per 100,000:
Suicides in England and Wales - Office for National Statistics (ons.gov.uk) Far higher than your 0.16 per 100,000 and less than 30% lower than the USA's figure.
Given the US's male suicide rate is approximately double the UK's.... yes, a lot of them might well still be alive. Suicide by firearm is a lot more straightforward, and irreversible, than many other methods.
Hanging is the commonest method here. That's pretty straightforward and irreversible too. Lack of access to affordable medical care for people in a mental health crisis has to be a big factor in the USA.