In any risk pool, the less risky participants subsidize the riskier participants. It's simply the nature of risk pooling. Public or Private really makes no difference in this regard.
This is the current system remember we pay for everyone who is uninsured now. With single payer national healthcare everyone carries everyone. I am guessing you already knew that but were hoping to fool someone less informed than yourself.
I bet Chuck knew that too...
In a boat at sea one of the men began to bore a hole in the bottom of the boat. On being remonstrating with, he answered, "I am only boring under my own seat." "Yes," said his companions, "but when the sea rushes in we shall all be drowned with you."