Is there any evidence that double blind peer review systems are beneficial?
Yes, there is scientific research on this topic. 

Using data from ACM WSDM'17, A. Tomkins et al. showed that double blind reviewers are less likely than single blind reviewers to accept papers from famous authors, top universities, and top companies.

See: http://www.pnas.org/content/pnas/114/48/12708.full.pdf

Update: As mentioned by @thomas-supports-monica in the comments, there is some evidence that the article linked above may have some issues. See https://papers.nips.cc/paper/8770-on-testing-for-biases-in-peer-review.pdf .