Given how complicated the brain - and its interactions with the body - is, and even how many successful medical interventions depend on placebo effect, it seems reasonable that the approach of "try it and see if it works for you" is quite effective.
I think it's just common sense. Sure, we could wait for science to prove XYZ fact about meditation...but if it makes you feel better today, why wait? You might be dead by the time the study comes out.
Sure, but my point is that this works beyond the expectations of "common sense".
The XYZ fact may turn out to actually not generalize. With mental phenomena, often how you got somewhere matters more than the thing itself. For a nice negative example, think about taste - many of us have strong repulsion towards some foods caused by random events in the past. Like, for many years parsley made me nauseous, and it started when as a kid I ate a broth and then threw up. It's a common thing that when you're sick your brain can create associations between how you feel and what you smell or eat. So you end up hating some food not because it's objectively bad, not because everyone else hates it too, but because of a random event in your life that happened to get associated with it.
I treat n=1 experiments as a way to probe such random associations. If you find out that something works for you, it doesn't matter that it isn't scientifically proven. It doesn't matter the effect doesn't generalize. It doesn't matter it works only through association and that this association was created due to you doing the experiment. If it works for you, it works for you.
But to be clear - "it works for me" is the only thing you can say in such case. N=1 experiments are ok, but trying to generalize from them isn't. Saying "it must work because it worked for me" based on such experiment is of course quackery.