All suicide methods should be public property, in my opinion.
Firstly, as others have pointed out, it may provide easy access to effective suicide methods to people, who might otherwise have chosen a very gruesome method.
Secondly, on of those very gruesome methods could be being hit by a train, which involves other people involuntarily, which is unfair - so access to an effective method can prevent innocent, involuntary bystanders from participating in someone else's suicide.
Thirdly, no one chose to be born, so we are all basically living out an 80 year long prison sentence that our parents saddled us with. Now, it's our right to end that prison sentence by ending our own lives.
Fourthly, we have no way of knowing who anyone is, or how old they are, so there's no way of filtering out under-age people, for example.
In my view, the right to die is equally as important as the right now to die by someone else's hand. In other words, no one should fear being killed, and no one should feel compelled to live against their will.