I know this was in the plans at some point, and when 9/11 happened it got put on hold and then eventually killed altogether. From what I understand, there was a new requirement for offset distance between base property (?) and a road like that, and there was no route that could be found. Maybe that's not accurate, and if others know better I'd love to hear. BUT I have some work related to Ft. Belvoir in northern VA - another base that got a lot of growth due to recent BRACs. And if you look at the map, Rt 1 - a MAJOR road in that area - cuts directly across the base. And it isn't far from major buildings.
Just imagine the benefit of a road across the base, connecting the southern part of the parkway to either Zeirdt Rd or even 565. The traffic along the Parkway would be reduced tremendously at times (think about those new baseball games, etc) - and more options are always great. As we are beginning to see, two roads from the Hampton Cove side of town over the mountain is becoming a serious choke point, and more growth just makes that worse.