Placebos are known to work. I neither overestimate nor underestimate them. I understand them for what they are: placebos. And some people actually need them.
Moreover, in social contexts, religion also "works" in many senses. A person asked me what me what can he do about depression and feeling of meaninglessness. Science would prescribe anti-depressants, medicate him and he would both have side-effects and the problem would never be cured. I suggested that if he were religious, the meaninglessness would immediately go away and he would need no medication, no external interventions.
So again, judging religion by "what can it do", it can successfully give people meanings. Which is quite non-trivial thing that science fails to do to many people. So religion can be presumed to be acting on some truths regarding what drives and gives people meanings. Religion successfully demonstrated an understanding of that, you don't need statistical analysis or peer review to see that, it's plainly obvious. That knowledge just doesn't carry on to other stuff like how celestial bodies move, and there's no reason to think it does.
I love how you're the spokesperson for "science".
Ironically, when you look at how you describe the merits of peer review, you sound quite like an instrumentalist yourself.
Also quite ironically, the new science religion keep on pushing this funny narrative that science is about "being wrong all the time" which is like the complete opposite of scientific history. All of the established science is just the successes. Look at the great physicists. There is no mistake in Newton's laws. Or in Einstein's. They are just as valid today as they have been back then, in the areas where they were demonstrated and studied.
How did we reach this apologetic science? "good scientist will be wrong all the time"? That sounds like gaslighting scientists in a failed system rather than accurate historical statement. Science advances because someone eventually succeeds. In the grand scheme of things, there are no mistakes. There are corrections, there are expanding the domain of applicability. But the mistakes are sent to the trashbin of history, and if a failed system decided to gaslight you into rationalizing failure, stop listening to it and start seeking success.