Mechanical support is what family members see. When they are told it is a temporary measure to mechanically support breathing, and they see a machine, it sinks in. Having dealt with my family members who are not medical in any sense of the word, they understood the explanation. When ventilation is explained to family as life support, it really means without ventilation there is no life. Most people anticipate some form of recovery when they see a vent. Unless you are a nurse, then you may see it as the kiss of death.
When initiated would you call it organ support, if the expectation was recovery? As a lay person it would be easy to confuse, and they will ask which organ.
I pray I never have to deal with this again in my life time. If I do I do not wish to hear organ support. I don't want my loved one to be considered cadaver, and I do want them respected in every way. Modesty needs to be maintained. Appropriate conversation at the bedside, etc.
Being on the other side of the blanket, as it were, being the family member, I saw these things. While they were minor in the whole situation, I knew my loved one would be mortified to have people see him striped naked. Care is needed, and that includes caring about the person who did inhabit that body.