Using my highest level (SDE) connection, there are some fields I cannot delete in many of my older feature classes. They are all old (SDSFIE 2?) primary keys, I think, but I see nothing different about them in the field and table properties. They are not used in indexes, participating in relationships, subtype fields, or otherwise special.
The data has archiving enabled but not edit tracking or replication.
Who is the data owner of the table?