It's scary that such war-time measures are being taken. It's as if serious aggression was imminent. I think when you need such measures and there's no war going on or imminent, you're doing something seriously wrong.
Second, the capital (especially around the Pentagon) is always covered in missile defenses, as well as every other kind of defense they can think of. Also, not all members of the Cabinet ever meet in one place https://en.wikipedia.org/wiki/Designated_survivor and lots of other super-defensive stuff goes on all the time.
Third, it looks like this has mostly been a research project so far, and the D.C. deployment is going to be a way to show it off.
http://www.propublica.org/article/who-are-we-at-war-with-tha...
"[We're] getting away from the Ph.D. engineer types running the system to the 20- or 25-year-old soldier running the system."
"D.C." is also good because it has a lot of airfields, many quite busy. Immediately adjacent are Reagan National; Bolling is now helicopters only, and there are a lot of helicopters flying around (at least a lot flying around Arlington, world HQ for the US military among other things). Further out you get Dulles, BWI and Andrews. So the "blimps" will have a lot to track.