The message you receive when you can't delete an issue type is this (refer to JRA-17949 for steps to reproduce):

In order for an issue type to be deleted, it needs to be associated with one workflow, field configuration and field screen scheme across all projects. If this is not the case, JIRA can not provide a list of valid replacement issue types.

This did not make much sense to me on first viewing, and I'm a JIRA developer. I tried to look for more information in the docs, but nothing seemed to touch on it.

This screen could definitely benefit from a help link or more information explaining why exactly the issue type cannot be deleted, and what the situation would need to be for it to be possible.