Well for their information - the covered terrace area that surrounds Walter Reed Army Med Center (WRAMC) is also a “No Hat, No Salute Area” the initial reason for that rule is there are so many Docs/nurses(officers) that you’d break your arm just walking out. However, since I’ve been down to WRAMC, given the neighborhood that surrounds it, maybe they too are afraid of snipers.
Maybe somebody can calibrate me here, but I recall hearing that the big open courtyard in the middle of the Pentagon is also a “no hat / no salute” area.
Again, merely for practical reasons. With so many of various ranks milling around it would look like everybody doing jumping jacks.