The worst responses would not be from people with healthy immune systems, because the cytokine storm is an event apart from the normal immune response. The strong innate response is one thing; the overreaction is another.
I’m not a scientist, just a patient with an autoimmune disorder. I can get over a cold or fight off infection from a cut, but my body is predisposed to overreact to any infection by attacking the lining of my heart, thus I have chronic autoinflammatory pericarditis. Only a combination of anti-inflammatory drugs and immunosuppressive drugs keep the response in check.
It’s no different from why I can eat peanuts without my system overreacting, while others with an allergy would die from it. People with compromised immune systems aren’t “allergic” to this virus, but by the time their slower innate immune systems kicks in, their bodies are screaming for a stronger response and are more likely to suffer an overreaction than someone whose system fights it off in the first few days.