I tend to agree with you, but am reminded of three facts:
1) Mental illness can and does become a life threatening condition for many women. Aside from accidents, suicide is by far the number one cause of death for women of childbearing years (according to the CDC). And some of those "accidents," when examined more closely, may not have been quite so accidental.
2) Mental illness is often very difficult to diagnose without the benefit of a doctor's extended access and close personal relationship with a patient.
3) Medical marijuana, prescription drug, and insurance fraud fiascos have all demonstrated that hospitals are full of dishonest doctors who, for the right price, will diagnose anything a patient requests. And, as a lot of conservatives have pointed out, mental illness is a lot easier to fake than a heart condition.
It seems to me that the ultimate morally consistent solution is to outlaw all abortions, and provide better care and assistance to all expectant mothers who need it.