Any responsible doctor/practice/hospital will have life insurance to cover expenses resulting from the death of a senior employee such as a doctor. It may even be bundled into the doc's malpractice insurance.

Executors execute wills. They are responsible for the disposition of the dead's assets, not the continued care of patients.

You don't need to prove that you "need" any prescription. If your doc dies, your current prescription is still in effect. When it comes time to renew you need to find another doctor. You don't get to carry on with a prescription forever without medical supervision just because the original doc is dead. It is not up to the patient to decide what they "need" when it comes to prescriptions. Input yes, but the decision as to need is the responsibility of the doctor.