Officials have no duty to save or protect his life at all, nor do they have a duty to save or protect anyone else's life - ever.
It's totally, completely voluntary on their part, whatever they feel like doing at the time - save him, kill him, whatever. And whatever they choose to do, they are not personally responsible for their actions. THAT'S the law.
There are people walking around below. So yes they do have a duty to get this idiot stick off the building.
That is private property. Are you going to tell me they don’t have an obligation to remove him if the owner asks them to?