I'm certainly open to the idea that Ivermectin might do something, and since it's essentially harmless and normally used to treat all kinds of parasitic infections in humans, I fully believe that a COVID sufferer has an absolute right to try it. (Were not talking about poisonous chemotherapy drugs, so the risks are minimal and certainly consistent with the kinds of risks that we expect individuals to routinely judge for themselves.)
I do agree with you, though, that there may be a placebo effect here or worse, just a coincidence. People recover from long COVID, so how are we to know that the recovery wasn't just coincidental? The same phenomenon is at work in a lot of areas of medicine. Consider back problems and herniated disks. If you herniate a disk and are in severe pain, you can be evaluated by your physician, be recommended for surgery, have the surgery, and do physical therapy, and in around six months, you'll fully recover. In the alternative, if you show regular improvement, you can wait and recover. Did the surgery actually improve your condition, or did time improve your condition? Who can say? (I mention the example because I personally experienced the problem. I had a herniated disk with nerve involvement so extreme that I had flank spasms mistaken for a potential kidney stone. After relief of initial pain and a course of muscle relaxers, I wore lower-back supports and experienced a gradual improvement over seven months. I had an uncle with similar back problems at a similar age, and he opted for surgery. Surgery comes with post-surgical restrictions on movement essentially identical to the restrictions imposed on me by the back pain and that I followed out of necessity, and the recovery involved physical therapy with a recovery timeline of around six months. In my personal experience, the recovery without intervention was identical to the expected period of recovery with surgical intervention.) The fact is that when we're suffering, we have a bias toward action to correct the suffering, and when you do something and an effect coincides with the action, you can easily reach the mistaken conclusion that the action caused the result, a result that may have happened as a part of the normal process of recovery.
I think that a lot of people fail to understand the basic idea in this case. You can't take one example of a person taking Ivermectin and recovering and conclude much of anything. People recover all of the time both on and off Ivermectin. How do we identify real effects if you cannot confirm them from individual responses? You have to look at large populations and search for statistical evidence of an effect.
With Ivermectin and other treatments, I'm not so sure that there are meaningful studies to support an effect. To be fair to the believers in Ivermectin, I don't think that the powerful are allowing the studies for fear of vindicating the faith of the dirty masses, and they should allow the studies. The best way to restore trust between people of different levels of expertise and understanding would be to encourage large-scale studies and make the results available for all to see. If Ivermectic be ineffective, you won't persuade all of the faithful, but an openness to investigate, a willingness to risk being wrong, and the humility to admit the possibility of error or actual error would go a long way toward convincing the persuadable who rightly wonder what supposed experts have to hide.