To sum up, peer review works well as a minimal gatekeeper for scientific publishing. Researchers who have good work rejected can simply try again without too high a cost. Bad papers make it through, but generally sink without a trace under the volume of decent papers. Excellent papers tend to float to the top eventually.
For grant proposals, on the other hand, peer review only serves to get rid of the so-bad-my-pet-monkey-might-have-written-this applications or those that are obviously misplaced. “Don’t ask for money for quantum information research from the NIH” is a lesson that, you would think, should not have to be taught. But that seems to be as far as it goes. From there on, I don’t think it helps much, and it may actually harm in terms of the substantial amounts of time lost.