People choose the easiest tool available to them. A common method in Europe is a belt to the doorhandle which is more painful and slower than a bullet. Removing tools does not prevent the outcome, just increases the suffering.
As a counter point though, different suicide methods have different fatality probabilities. Handgun to the head has a really high fatality probability, rope to the neck less so. Removing a high fatality suicide method could cause people to turn to a less fatal method.
You sound like an efficient assets manager. People turn to a suicide because their life is miserable, often for objective reasons (e.g. cancer) and you may find it hard to believe, but it's their right to end it.