Well, science has nothing helpful to say about things we don’t have any good reason to think exist, like the supernatural. So, not a criticism of science per se.
The fact that science is limited both in sociological and in epistemic terms is well known. It remains a fact that it is pretty much the only tool we have not just to observe, but to understand the world. No other approach has done anything even remotely close to it.
We already know — because of science — that EGR is limited and will need to be superseded. And, again, the only way to do that is more science.