Financial interests are as likely to be those of relatives eager for their inheritance, and eager not to see their inheritance spent on an elderly relative's medical care, as of third party payers. And while getting the government out of the picture as a payer, and as a regulator of private payers is urgently needed, there will never be a complete elimination of third party payers in a free country. People buy insurance and then the insurer is a third party payer.
I know there is a moral hazard, but the insurance company is obliged to pay according a prior contract. Only insofar as it tries to weasel out of its contractual obligations does it adversely influence the medical decision (or try to). This market solution to the problem is not to patronize unreliable insurance companies. The problem of grasping relatives is likewise to be solved in advance by one's medical directives and one's will.