This post will be updated as I'm corrected, criticised, made aware of more content. You can help.
Since no identifies are involved, there are less chances of a bias due to known authors or institutions (in theory).
Reviewers can review work by people they have previously worked with (provided they cannot discern identity from the work itself).
Since reviewers identities are not known, authors cannot hold grudges or bias (or favouritism) against specific individuals based on their reviewing. e.g. Gender-bias or Racial-bias
If rebuttal is used, the authors can be more critical of the review without worrying about personal repurcussions
Is it possible to truly hide my identity if my work is in a sufficiently niche area? e.g. I work on GDPR and Semantic Web
Is it possible to effectively hide that I have authored the past work re-used in the paper? e.g. If I use A, B, and C (references) all authored by one person, will it not be evident that I must be one of those authors?
For resources such as source code, I have to create a non-identifying copy for the paper. e.g. I usually put my name and email in files I author (in the header section), or put the URL for the repository such as Github, or put names in comments regarding more information or Issues or TODOs. If I supply this code with the paper, I have to find and scrub such references.
For information hosted on institution infrastructure, I have to find alternative means of hosting. e.g. If I have documentation and manuals associated with my work on my research group's website, I have to find and segregate relevant sections, and host them elsewhere where they cannot be used to identify me.
For demos and executables hosted on institution infrastructure, I have to find alternative means of hosting. e.g. If a particular service runs on university VMs, which is part of a demo presented in the paper, then I have arrange alternative non-identifiable hosting solutions (such as AWS) to host the demo. Additionally, I have to scrub any identifying information from the demos such as names, contact, university, funding.
Iterational updates are difficult to anonymise e.g. presenting v2 of some work is unlikely to be authored by someone not involved in the previous work
Authors don't know who the reviewers are, so cannot hold bias or grudge against them
Anonymisation of author identity is not required, which requires less changes or work for the authors to prepare their work for presentations. e.g. software code can have identifying information
Reviewers can be critical of the work without worrying about personal repurcusions. e.g. Grudge against a reviewer because they did not accept the paper
Reviewers can look up previous work by the author which can assist in evaluating current work
Reviewers know who the authors are, so can be biased or influenced. e.g. one of the authors is a well-known or popular persona in the field, and so adds an 'invisible pressure' to automatically accept their work. Can also be specified as "identity validates work".
Reviews are transparent which can encourage more quality in terms of the review itself e.g. being specific and not vague in referencing issues, or being more civil in language
Reviewers may not feel comfortable being more critical of the work because their identities will be known
Reviewers may not feel comfortable being more critical of authors well-known or popular in their fields
Authors may hold a grudge or bias against reviewers e.g. based on gender or race
Reviews can be assessed by all parties, including non-authors, which motivates more quality in reviews.
Corrections can be found and made in the future.
Authors and Reviewers may not feel comfortable sharing more critical reviews.
Others can reuse or adapt existing reviews in other reviews e.g. re-using someone critical argument's of an approach in an review
Authors and reviewers may not be aware of the best license suited for reviews e.g. CC-by-ND may prevent some re-use of reviews
One or more reviewers discuss in a forum-style about the work, and collaboratively or individually submit reviews.
Discussion between reviewers can lead to better reviews in terms of clarifications and justifications
Reviewers may not be comfortable discussing their opinions with others, especially if identities are known
Reviews are associated with specific versions of a manuscript, and corrections to the manuscript address which issues in reviews have been address i.e. reviews evolve as the manuscript evolves.
Reviews are always relevant to the specific version of the manuscript
Progress of work can be assessed more systematically
Results in more work for the authors and reviewers, or editors in terms of maintaining information