Is it ethical for a physician or any other health care practitioner to prescribe or administer a medical treatment just to pacify an anxious or demanding patient?

Drugs should only be prescribed or administered for the benefit of the patient, not for the convenience of the physician or health care practitioner. That said, you should be aware that people do not want to feel excessive anxiety, and it is quite common to prescribe drugs to treat anxiety, But you would not prescribe a drug because the patient is demanding. That is not a medical problem, unless the demands are of a hallucinatory nature, indicating that the patient is schizophrenic, in which case you could treat the schizophrenia with an anti-psychotic drug.