I’m not sure what the bias is here - maybe halo effect? - but the issue at hand is that the antibiotics are being used in a scenario where they cannot be effective. They are, in that way, a placebo to the same degree that homeopathy is, despite any other properties outside of the acute situation.
Say I have some really great tasting distilled water. Perfectly pure, exactly what I need if I wanted to quench my thirst. Now, I also have an empty gas tank.
Should I put water or flat Coca Cola in the gas tank? They are both bad, despite the separately superior qualities of the water. Or, maybe a better comparison is putting diesel in vs coke. They are equivalently bad for the engine despite one of them being used for a similar but separate situation.
Your metaphor is does not work well because water and coke are both pernicious to a car. A better one would be quelching thirst with water versus coke. Both will calm thirst, and are reasonably “neutral”. The second has pernicious effects, especially in some people (diabetes for example)
Distilled water has other uses besides drinking. It can be used in chemistry for example. You would not get good results in chemistry if you replaced distilled water with coke. “I can drink water, surely I can use coke instead of water on this chemistry experiment, because I can also drink coke” is clearly faulty logic.
And yet, that’s exactly what people do with homeopathy.
While it should always be presented as a “complement” to medicine(because it can have some mental/placebo effect in some people, in some cases), very often people take it as a substitute (the marketing word is “alternative”) to medicine. This is something that the homeopathic industry can’t help but “allow happening”. In fact they are motivated to promote that way of thinking. First it increases direct sales. Secondly, the more mixed up their product is with medicine, the stronger the placebo effect will be, and that will increase sales further.
Unfortunately the placebo effect is very limited. You can’t mend a broken arm with placebo alone. You can’t cure cancer with placebo alone. And yet people replace chemotherapy with homeopathic “remedies”. And then they die.
In short: doctors should never give homeopathic remedies, because that puts them on the same level as medicine. That will ultimately make some homeopathic makers richer, but it will also get some people killed.
Say I have some really great tasting distilled water. Perfectly pure, exactly what I need if I wanted to quench my thirst. Now, I also have an empty gas tank.
Should I put water or flat Coca Cola in the gas tank? They are both bad, despite the separately superior qualities of the water. Or, maybe a better comparison is putting diesel in vs coke. They are equivalently bad for the engine despite one of them being used for a similar but separate situation.