There are not really any differences in how private health insurance markets work.
I think any scholar in health policy would tell you that those are how health insurance markets work unless government forces them not to. Unless government regulates private health insurers and forces them not to drop the old and the sick, that is what will happen.
My aunt lives in New Zealand, the country I am from. She bought private health insurance as a school teacher for her entire life. At 80, she's finally in hospital. They asked her the last time that she was in hospital, and she said 1928, when she was born. At this point in her life, when she finally needs her drug insurance coverage and her private health insurance benefits, she can no longer afford them because they are too expensive. She contributed her whole life for nothing.