Actually, the insurance company would probably do some checking and, finding the proof that you were diagnosed before taking out the policy, would invalidate your policy based on your "fraudulently" filling out the application - and pay out nothing.
The example still works even if the guy is diagnosed after taking out the policy.
Bob takes out a policy because it seems like a good idea, and subsequently is diagnosed with Expensive Heart Disease. He holds onto his policy with dear life, prioritizing the premium payments over things like dinner if he has to.
Joe takes out a policy because it, too, seems like a good idea. Nothing happens to him, and six months later he has a change of heart when he thinks about how many shots of tequila he could be buying with the premiums instead, so he cancels his policy.
Thus sick people become ever more concentrated in the pool of individual insurance customers.
