I think your analysis is a little bit vague? There are an almost unlimited number of chemicals that might be tried to treat any given disease. You can't test

I think your analysis is a little bit vague? There are an almost unlimited number of chemicals that might be tried to treat any given disease. You can't test all of them. If you limit the chemicals to those available at a vitamin store (which is how I'm interpreting 'nutraceutical') seems like a terrible strategy for how to deploy research resources. Almost no diseases are treatable in an effective way with these chemicals, and when there are positive results in a study involving these chemicals it is almost always not reproducible or the effect of the chemical is insufficient to justify using it. The vitamins and nutrients which we have evidence there is a benefit to taking are already added to almost every food product you can buy. The only people who seem to be motivated to push this strategy are the companies which profit from selling big plastic bottles covered with the most misleading claims they can legally make, and filled with what are basically placebo pills. I'm going to go ahead and make a prediction: There is nothing you can find in a vitamin shop, taken in any amount, that will end up demonstrating sufficient benefit to the treatment of COVID that it is worth using.