No, it's the opposite. People with free healthcare are more likely to attend their GP regularly and detect diseases at an earlier stage when it is cheaper to treat.
No, that makes them more likely to seek free treatment for the illnesses they have caused to themselves. That's a different point to the one I was making.
If we knew that if we became sick and were unable to work we'd starve then we'd be far more careful about doing things which were likely to make us get suck.
If we knew that we'd have to pay the full cost of cancer treatment we'd be far less likely to smoke or get fat.
If we knew that we'd have to pay the full cost of diabetes treatment we'd be far less likely to get fat.
I'm not suggesting that we should construct our society on that basis, I'm merely pointing out a negative consequence of how we currently have things constructed.
The moral hazard is there because there are two parties in the transaction, the State/taxpayer and the consumer of the healthcare. One party, the State, cannot control the actions of the other party, the consumer of the healthcare. Therefore the State cannot control the amount of healthcare the consumer needs to consume of chooses to consume. Given that there is a limited amount of money and human resources available in any healthcare system the person who becomes unhealthy due to their own actions (smoking, bad diet, lack of exercise, obesity, addiction etc) is consuming healthcare resources that could be consumed by people who are unwell due to factors beyond their control.
In other words if you're diabetic because you're fat and lazy or you've got cancer from smoking then you are partially responsible for the waiting times for operations for children with scoliosis.