If what you describe in your first paragraph is true, I find those reasons and actions maddening.

Mainly because when someone actually takes his/her own life, that person was at the very least in an unstable state of mind when making the decision and fulfilling the plan. And when people are desperately unstable (even for a brief period), law enforcement and other emergency personnel are usually permitted to (and sometimes required to) assume control over the person and get them to a facility to be involuntarily evaluated.

So, because a person is able to avoid detection/interaction with such personnel before they are able to complete their suicide act, then they have the "right" to remain unidentified?

But if, say, a cop walks into a hotel room right as the person is cutting their wrists, the individual can just say "it's my right to take my life and to not disclose my identity, please see yourself to the door"?

No, the officer is permitted (ordered, even) to subdue, disarm, and save the person. Philosophically, we can't have it both ways. The state of mind of the victim in the scenario I describe here doesn't change. Only the circumstances of discovery do. My stance is that just because a suicide victim desires to remain unidentified, we do not have to and should not "honor" that request. We need to treat this person just like we would treat them if we had been able to intercept them in the act: as a person in a psychological crisis who isn't capable of contacting their family or coping in general on their own. I didn't mean any of that to sound harsh or demeaning. My point is that we intervene in mental health crisies because the person isn't able to make appropriate decisions on their own during such a crisis, and a "successful " suicide is no less deserving of our intervention.