This is one reason I'm in favor of government health care: The profit motives of private health care favor denying care, since not paying out money is a good way to make money. So you have case where nobody will cover you for arbitrary reasons, or deny you payment due to a "pre-existing condition" or some other nonsense.
As for power lines.. well, there haven't really been any conclusive studies in this area. But you get the point.
Same-environment shouldn't be a factor, as long as the reasons the environment might impact health are/can be known.
I'd argue that nobody should be living somewhere that might have health risks involved (e.g., underground oil spills, toxic ash, a radioactive waste storage facility a block away from the elementary school .... in other words, williamsburg/greenpoint brooklyn).
This is an argument against all private insurance (home, auto, etc).
Would you favor the nationalization of all types of insurance or just medical? Doesn't auto-insurnace have the same evil profit motive?