As far as I know (from gameplay), they take manpower to construct...why do I have to mobilise to create these installations?
I guess that's a flaw in the game's mobilization system, then. Really, demobilizing should push you back down to whatever level of conscription you were at before, with a little bit extra manpower from the soldiers staying on. Why not just add some manpower in your savegame? That would seem perfectly reasonable.
Remove a division or two that you don't need. It should give you a lifetime supply of nuke plants.