I strongly disagree - I think it is vital for a civilian to lead on defence, and preferably one who comes at it 'fresh'. The reason being is that Ministers will come without baggage, and be willing to question sacred cows and ask hard questions. This encourages people to really think about why something is happening or not.
To bring a military guy into post would merely put someone who has spent a career thinking one way, and who subconciously probably has a series of biases or views, which they are less likely to question.
Frankly, if the military are unable to make a good case for themselves when briefing new Ministers, then they should ask whether this is the fault of the Minister, or their fault for being unable to articulate clearly what they need.
As for culling bureaucracy, my experience is that the Armed Forces excell at creating it, not cutting it!