No one does. No one should.
I would suggest donations be sent TO Walter Reed, in care of the hospital, etc., bypassing the Red Cross entirely. For that to work however, and given security considerations, it would take a point man to handle the packages. And that would be the name on the address. Maybe somebody could contact folks, there, and see if there are any volunteers. Then those who don't want to send ANYTHING to a Red Cross address can still send needed items directly to those in need.
I agree with your suggestion. But with security problems, etc., a point person or group is needed for clearing the packages and making sure the RATs haven't sent any nastygrams to our soldiers there.
Not all Red Cross volunteers are like the European versions though in my opinion. I'd never give them money anymore because of my fear that it would be forwarded to the International group or Red Crescent but phone cards that only can be used in America and other gift items are okay, I think. But that's just me.