I know in clinical trials they'll ask participants which group they thought they were in. I wonder how accurate it would be if they asked what author a reviewer thought they'd reviewed.
If there's anywhere that bias needs to be reduced, it's in the grant awarding process. I'm not entirely sure how big a deal it is in publishing. I'm sure it exists, but eventually, if your paper is good, it's going to get out there, even if it's not in the top impact journals. In this day and age, what's the difference. As long as I can read an article and judge it on my own, I could not possibly care less who publishes it. Remember, the Lancet is the journal that published that rubbish about vaccines and autism. Meanwhile, plenty of high quality research is published in journals whose impact factor is ~2. The grants thing is way easier said than done.
My old mentor said a similar thing, of the need to blind authors and journals during grant approval (on the topic of publishing in eLife / PLOS). Later I heard a professor claim that the NIH already does something along those lines, but I was never able to find a primary source to confirm that... (annoying, my search results were drowned out by grants relating to blindness in the visual sense)