The thing about personal choice is that, well, it's personal, and is affected inevitably by your state of mind. I fundamentally refuse to accept that, except in cases of unbearable and continual physical pain, anyone who wishes to die is in a right state of mind. Even then it's hard for me to imagine, but I'll reserve judgement on that until I ever have to deal with it personally.
This question wasn't really about those special cases, but about the idea in general. Should anyway be able to kill themselves unchecked and unchallenged? Well, at some level they are, I suppose. I'm sure if I put my mind to it the knives a few feet behind me could be fairly effective, and no-one could stop me. I wouldn't actually do it, or at least I hope not.
Suicide in general, though, from those people who have what are fixable problems, is just, well, something that should be stopped if possible. Many, most, of those who kill themselves did have friends, family, neighbours who will miss them and be affected by their death. Certainly those who kill themselves in public ways affect deeply all who witnessed it. It is, I think, a deeply troubling and, well, selfish act. Those who must live on in the knowledge that a loved one died, and that it need not have happened, may never get over it properly.
So yes, it should if possible be stopped. And if ever someone wants to commit suicide, you'd better be sure they have absolutely no other choice, no reason to live on, before you even think of helping them to do it.