How did they prove the idea that statistics is an effective research method

The intimidating complexity of the brain doesn't turn it into a strange, otherworldly realm where the same boring laws of physics somehow cease to apply.

Where's the research on producing better and permanent placebo?

Your idea of what a placebo does is very confused. A placebo is not a backdoor fix to reboot the brain with a secret magic word. A placebo is anything that is physically ineffectual but resembles actual therapy, and the only reason why it's still a necessary evil in research is because it gives a standard of comparison to ascertain how much of the effect of an actual treatment was due to mere suggestion. It is (outside of rare scenarios where a doctor is in an extremely precarious situation with no viable therapy at hand) the epitome of unethical to prescribe a placebo.

Depression is a real thing, it's just not a hardware problem.

Unless you're a dualist, every mental disorder is a hardware problem. There's simply no other place where things can happen.

If you think medicine is a better fit for the human brain than a computing metaphor

Don't put words in my mouth. I've never spoken against the computing metaphor.

You can observe their results on Youtube.

I can also observe faith healing and exorcisms on YouTube. Show me large-scale, randomized, controlled trials published in peer-reviewed journals.

You will not find one person [...] to hang on to anything diagnosed as depression after ten orgasms in half an hour.

Now you're making a testable claim. You're saying lots of orgasms cure depression. What's the scientific evidence?