There's a lot of things wrong with what you are assuming, and assuming that the DOE adds massive bureaucratic overhead is a bit naive, frankly. The NSF doesn't

There's a lot of things wrong with what you are assuming, and assuming that the DOE adds massive bureaucratic overhead is a bit naive, frankly. The NSF doesn't have a physical presence, and given that particle physics is a very natural extension of nuclear physics, that's why the DOE does particle physics (which includes lightsources). DARPA is purposefully limited in scope, they also have very few facilities (really, they are sort of like the NSF for weapons). Nuclear Weapons research is a small (but very important) part of the DOE's mission, but weapons and reactors are so closely tied together that it's really impossible to separate the too. There's certain levels of civilian and military separation that have been put into place by law. Many of the labs do weapons (usually conventional, only two do nuclear) research, many do only science, some do both, some do reactors and some do accelerators. The DOE services everyone though, defense, civilian, academic, everything, and that's largely why they are there and set up the way they are. It sort of ends up being this buffer zone between pure science and defense, and that's generally a good thing I think.