In general you are correct but sadly there are perverse incentives even in a system like the NHS. There are two problems. (1) treatments are approved only if they make financial sense for the country and (2) sometimes those calculations go wrong. At one point people were being allowed to go blind based on a cost calculation. Even though letting people go blind was more expensive overall to the country. The cost of treatment to the NHS budget was greater than non-treatment but the social care costs came from another budget.