The alternative is far worse. When people have to pay for something, they don't use it unless they absolutely have to.
When it comes to health, this leads to higher death rates from preventable illnesses and worse health outcomes.
In point of fact health care is the field where triage was invented. An important principle of health care is to assess how to assign limited resources to those who need them most; people abusing the system will simply have to wait until resources are freed.