The more is revealed about the identity of authors and reviewers, the less honest the review process may be. Such openness may favour already-established scientists over newcomers.
In the ideal world a reviewer would raise the same concerns when reviewing papers from a Nobel-prize winner or from an undergraduate student. But as people are even afraid of asking possibly dumb questions in public, I would be really surprised if they could apply the same scrutiny regardless of who they are reviewing.
Even with the standard (single)-blind process, I heard that an already-famous scientist submitted papers under made-up names to receive honest reviews (just can't recall who).
An example from Herbert S. Wilf on a birthday speech for Donald E. Knuth (pointed out by Joel Reyes Noche):
In the 1980's, in the early days of the Journal of Algorithms, I was an Editor-in-Chief, and Don [Donald Knuth] submitted a paper to me, authored by himself under the pseudonym of Ursula N. Owens, ostensibly from some small college in some small nonexistent town in Kansas. The reason was that he really wanted to get a tough and substantive referee's report on the paper, and he had been finding that sometimes referees had pulled their punches because of his name at the top of a paper.
Double-blind process may be even more beneficial, but at the same time illusory (as topic, references and style may reveal the author). Moreover, the identity of the author may sometimes be beneficial (e.g., to compare if the new submission has something new).
None of it is a proof.
But instead of counting of lines of reviews, one can try to compare how softly (or harshly) are treated contributors, depending on their status (academic title, university name, fame/recognizability).