What makes you think that a hospital would bother to call Alcor or take instruction from them?
History. They don’t always cooperate, but in the majority of cases they do. The level of cooperation of standard medical personnel is a huge variable in the quality of a cryonic suspension, and can literally make or break it. Typically if the patient succumbs to a chronic condition then there’s sufficient advance warning to make all of the necessary arrangements to move them to a facility that’s knowledgeable about and sympathetic to cryonics, but in the case of accidents or other such sudden events sometimes things don’t work out so well. Once Alcor is aware of a member being near death or very recently deceased they react immediately and will generally go to heroic measures if necessary to fight for the patient’s wishes, but there have been several cases where uncooperative medical staff or family members have thwarted a cryosuspension. Shouldn’t you make room/free up resources for future generations? Why should you get to live forever? This is probably the single most offensive obje