Given this is a hypothetical scenario, why drug someone with sedatives when this drug has not proven ineffective?
Huh? Her issue, as you phrased it, is not actual risk of Covid infection but the anxiety the situation is provoking. Treating the anxiety with meds or a referral to mental health seems the proper course of treatment rather than issuing a prophylactic medicine that has no proven benefit AND is in short-supply.
Your focus on one narrow aspect of my hypothetical patient's needs demonstrates why professional judgement is important.
No, your narrow focus on "I can make that professional judgement if I want to" is clouding your arguments. You don't seem to be considering all the other factors that should help you decide whether or not to prescribe plaquenil. To wit:
Straw man. Obviously if my hypothetical patient was able to fill the prescription, there wasn't a shortage.
Just because a patient was able to pick it up does not mean there isn't a shortage. What the evidence (the scant anecdotal evidence there is) shows is that it's most useful in treating people who get the disease, especially the most severe cases. If all prescribers thought like you (and, obviously a lot of them do) and prescribed it to non-sick patients -well . . . what good is it doing sitting in their medicine cabinets just in case when there are severe cases who could die because they can't get it?
Your "professional judgement" seems very narrow -it doesn't consider the larger situation we are in.
I totally disagree. It is not reasonable to prescribe chloroquine for a patient who has no clinical indication in a time when a shortage is happening and there are more critical patients who need it. And that's if the damn drug even works! What if the evidence shows it isn't really effective at all?

Are you suggesting you know better than said professionals? And you are arguing a straw man again.
It's not a straw man. Those prescriptions are being written today. If those professionals are writing prophylactic, just in case prescriptions for patients without a clinical indication or that fall under the FDAs emergency use authorization, then yes, I do know better than those professionals.
Not at all. Your position is that you can exercise your professional judgement and prescribe off-label. You describe a scenario in which you might prescribe chloroquine off-label. You justify that decision in the face of a shortage when critically ill patients might benefit from it more than your anxious patient without any clinical indication/evidence for the drug. Like I said, off-label in that situation is unethical, and quite clearly so.
Oh for pity's sake.
Dr Tiller was practicing in a state where third trimester abortions were legal.
OK, great. So we have a murderer who did not agree with the society's law because of his own personal ethical code. Surely, you agree that his own personal belief in the righteousness of his ethics does not mean that he acted ethically?