This seems a bit overstated. Its more akin to the head of NASA not having a space suit, or the head of the Olympics Committee taking 40 seconds to run the 100m. He is basically a pen-pusher at this stage, chasing funding, greasing up to politicians, attending banquets. I think it is good he cannot see secrets, he doesn't need to, he has staff for that.
I think you're underestimating how important classified material is in the day-to-day operations of the military. He doesn't have access to any classified material, even down to the CONFIDENTIAL level. Every U.S. Navy officer has at least a SECRET clearance as the "default," and a ensign would be hard-pressed to work without a clearance, let alone a 3-Star.
Another issues is some facilities require a clearance simply to visit HQ which often times is very well removed from the actual operations. When you can get a Campus Access Badge, often times pending adjudications like this can stop even that access. The whole system is rather antiquated.