Well I am one of the ones paying for it and I think it's a worthwhile use of my money because the basic health of the people in my country concerns me.
Hey that sounds great but how will you fund schooling for the kids of poor parents?
I am not a doctor so I can't tell you which diseases would be cost effective to test for. Additionally its not just testing for disease it's also vaccinations, education, and treatment. If you can discover and treat say high blood pressure with a cholesterol pill, that can save a lot of money if it prevents an emergency room trip for a heart attack. I don't understand why you equate preventative medicine with rationing.
I agree some people will never change certain habits but many others will. Look at the rates of smoking in this country over the last 50 years. What do you attribute the declines to if not education about the health consequences? Do you really not know anyone who has changed their diet, drinking/smoking habits, or exercise based on their doctor's advice? How many diabetecs do you think died because they couldn't be bothered with their insulin injections? Just because something is not a cure all does not mean it has no value.
This is incorrect logic to assume (if p then q) means (if q then p). Even if 3/3 single mothers live in poverty, that doesn't mean that any significant portion of poor people are single mothers. To make matters worse, you are further assuming that most single mothers are so because they were just plain irresponsible as opposed to death of a husband, divorce, etc.