Because the human psyche can very happily transform itself into a bottomless money pit when so inclined, and has been known to do exactly that, on many occasions, with alarming frequency.
If a rational measure of objective sanity doesn't satisfy a human being, will that person concur that their depression has been alleviated? Will they self-identify as mentally healthy? If an individual doesn't declare themselves healthy, was the money for the treatment well spent? How does a disagreement between a healthcare professional and an unwilling patient truly resolve itself?
This is an incredible position to take. People can complain equally endlessly about physical ailments as they can mental ones, all of your questions apply there as well. This does not mean that we should just throw our hands in the air at this intractable problem and say "welp, no healthcare for anyone!"
Just as in 'physical' care, a well functioning 'mental' healthcare system makes decisions about disorders, their severity, their coverage, incentives, and responsibility. Are we going to treat schizophrenia? bi-polar? general depression? psychopaths? divorce counseling? career advice? I put these in quotes because the line between what is a physical problem and what is a mental one is hardly clear... but just because something is more mental does not mean it's effects on society aren't enormous.
Structures need to be put in place to prevent patients and doctors from abusing collective insurance (over diagnosis, shopping for diagnosis, etc). This is a huge problem in both physical and mental health care, especially in highly privatized health care systems. Frequently occurring but less severe conditions may need to be incentivized (physical therapy is covered for X sessions in a year but after that the co-pay is much higher).
If a rational measure of objective sanity doesn't satisfy a human being, will that person concur that their depression has been alleviated? Will they self-identify as mentally healthy? If an individual doesn't declare themselves healthy, was the money for the treatment well spent? How does a disagreement between a healthcare professional and an unwilling patient truly resolve itself?