> That just opens the door to the driving version of "your grandma had cancer, so you won't get health insurance".

I think that highlights the stupidity of a privatised health insurance system. Not wanting to know about health problems due to a financial disincentive is not a sensible way of managing a populations' health, when typically prevention is much cheaper and more effective than waiting until obvious symptoms show up. I suppose it depends on whether profit is more important than the population's health.