The release notes of MySQL 5.6.6 (http://dev.mysql.com/doc/refman/5.6/en/news-5-6-6.html) – probably to be released very soon – say “INSERT DELAYED is now deprecated, and will be removed in a future release”.
INSERT DELAYED had several problems (search bugs.mysql.com yourself). IMO it always was a dirty solution substituting what should have been done 5+ years ago: change the protocol to allow ‘parallelism of multiple queries in a single connection’. INSERT DELAYED worked around it in some scenarios as the execution of such query was ‘passed on’ to another thread. But it was no real solution. We are still waiting for the real solution – true parallelism/multitasking in the client.
(MariaDB BTW has moved as far as possible in that direction without changing the protocol: A single client instance can handle parallel queries – but due to restriction with the protocol they will still require each their connection to the server).