While I understand where you are coming from and have no dispute with the examples you gave, this is not a fixed rule as stated.

Societies with collective health care, such as Hungary, the UK and Denmark (I pick these because their models are all somewhat different but there are many other countries) do not have more expensive health services even though there is no immediate payment. All have healthcare ‘free’ (i.e. not chargeable) at the point of service. All have healthcare that is generally cheaper than and superior to countries, such as the USA and many African nations, which rely on profit-based incentives to provide health care.

So, while I agree that delayed or insured costs will generally increase the expenditure, the power of collective assistance and the removal of profit incentive can mean that an abstracted charge leads to lower costs or better quality.