Any business that involves a substantial knowledge gap between the consumer and the provider is vulnerable to exploitative practices. There is a substantial knowledge gap between doctors and patients in the medical profession. This leaves patients vulnerable to exploitation.
If you know nothing about cars and you go to a mechanic for assistance, you are more likely to be ripped off. The same logic applies to healthcare. Doctors study for many years to become experts in human anatomy and illnesses. It is unrealistic to expect the general public to know enough about medicine to protect themselves from financial exploitation. The public will always be at a disadvantage. Some people will inevitably exploit this disadvantage for financial benefit.
A free health system does not automatically protect against exploitation. The margin for exploitation remains, and potentially increases. Under a publicly funded health system, the doctor or medical professional can still bill the government for unnecessary treatments. The government will then pay for unnecessary treatment from tax revenue. This revenue comes from the public purse, and the financial costs fall on the population at-large. If the patient isn't paying for the treatment they are receiving out of pocket, they are likely to be less vigilant to unnecessary or duplicate treatments. Therefore, the margin for exploitation could increase.
[P1] Industries with a substantial knowledge gap between the provider and consumer are vulnerable to consumer exploitation. [P3] The for-profit medical industry has a large knowledge gap between the provider and the consumer. [P4] Free healthcare removes the element of profit. [P5] Therefore, free healthcare systems remove the opportunity for exploitation.
Rejecting the premises
[Rejecting P3] Healthcare provided to patients free at the point of use does not necessarily remove profit from the industry.