<p>When I create an Issue Tracking list in SharePoint, I am unable to remove the Categories choice field that it adds by default as part of the Issue content type.  I looked in the list definition but I can't find anything explicit about not allowing the column to be deleted.  Does anybody know why the Delete button isn't showing up?  Is there a way to delete this field?</p>

I know that I have had a similar issue with field in a variety of fields where once the field is added, it is not possible to remove it.
Sometimes it is possible to create code to delete the field, but in most of the situations I have come across we have had to hide the field to prevent it from appearing.
This requires moving to using Powershell and the SharePoint object model to make the changes.
In most of our implementations, we have found it much better to create a custom solution with a custom feature that adds the custom lists and fields using the XML format for doing this. A list template can then be create exactly for what you need.
Doing it this way gives us more control over the result in a repeatable manner.