To respond to the original post - in fact a good E3 skipper will know plenty about "what is going on" and will be working with his mission specialists closely (primarily the Tactical Director).....While the TD will direct mission execution, the captain will take overall responsibility.
The system relies on a close working relationship between the TD and captain (particularly in an operational environment) but *it works*....I cannot think of a TD on the fleet who would like to see it changed (well one, but he has retired now)...