if health care is free people will seek it even when it is not needed
You have paid for your private insurance. Do you go to the doctor as much as you possibly could? When you are healthy, you have better things to do with your life, than travel the city from one appointment to the other.
When you're healthy, sure. That is not the only time you don't need a doctor.
The remarkable observation that medical spending has zero net marginal effect is shocking, but not completely unprecedented.
According to Spiegel in "Too Much of a Good Thing: Choking on Aid Money in Africa", the Washington Center for Global Development calculated that it would require $3,521 of marginal development aid invested, per person, in order to increase per capita yearly income by $3.65 (one penny per day).
The Kenyan economist James Shikwati is even more pessimistic in "For God's Sake, Please Stop the Aid!": The net effect of Western aid to Africa is actively destructive (even when it isn't stolen to prop up corrupt regimes), a chaotic flux of money and goods that destroys local industry.
What does aid to Africa have in common with healthcare spending? Besides, of course, that it's heartbreaking to just say no -