I'll ignore the fact that this makes absolutely no sense as a reply to the question you were actually addressing. Dimensio can take that up.
Instead I'll just take your statement by itself.
Obviously there's no single "observation" that "demonstrates" the validity of only employing naturalistic mechanisms in scientific investigation. Instead there are two primary reasons why this is considered part of the "nature of science".
However, if you don't find this reasoning convincing, that's fine. If you don't like the limiting of science to naturalistic mechanisms, then there's a solution.
No, the solution is NOT pissing and moaning, whining like a liberal about unfairness and dogma, on a internet forum. The solution -- the only solution -- is to actually DO some "non-naturalistic" science and show us how it works (and that it CAN work) successfully.
Scientists understanding of the "nature of science" will ALWAYS be modified to accommodate a genuinely successful scientific theory. History proves this.
For instance it used to be generally accepted as part of the nature of science that force could only be transmitted by "impact," that is by physical contact or connection between material objects. The idea of forces propagating through space was once considered "occult" and unscientific. But today, thanks to Newton and Maxwell and many others, science is full of "field theories" that address exactly such "occult" forces.
Why? BECAUSE THEY WORK.
The downside is that the ONLY way you can change basic assumptions, proven fruitful and universally accepted (at least in actual application), about how science works is by coming up with a THEORY THAT WORKS that requires these understandings be changed to accomodate the new approach.
If you'd prefer to continuing whining instead that won't help. Unless it just makes you feel better.