I see your point and I think your argument works on a case by case basis. No one really knows why we're alive and the meaning we give to life may not have any value at all. Like you said, the reasons for suicide are often subjective and highly personal. We have no right to determine whether someone should live or die and there will be cases where prevention will not work.

However, there are cases where suicide can be prevented because:

a. We know what the causes are.

b. They're affecting a large number of people and high rates of suicide could be detrimental to a functioning society in the long-term.

In developed countries like Japan and South Korea, the suicide rate is high due to some issues such as a wide economic disparity, excessive pressure at school, isolation, and exceptionally harsh expectations at the workplace (I do not know the actual figures, but this is an observation that has been supported). Consequently, the trend in these types of situations shows that the decision of to kill oneself cannot be entirely placed on the individual. The causes of suicide are not that personal because very similar situations are experienced by a large number of people.

Another point to support suicide prevention is that some causes of suicide, like depression, are not always permanent. If a suicidal individual is able to receive help and support to overcome depression, then they may be able to find their own personal happiness. It's worth a shot to help imo.