How does that work? You'd need trillions of them, even with FTL!
That's an area of space that's more then ten light years across. Even with something like ZPE, that's an obscene amount of resources to expend for limited strategic gain. You'd be better off using those resources to build a Dyson shell or a matrioshka brain. The former of which, I note, has only been attempted once at Hoshi no Iori, and that's only a dyson ring.
Why wouldn't they just make a swarm of energy gathering satellites, carpet a spherical area around their home system with them and use the energy generated to churn out a swarm of battleships and carriers. A much more flexible defense and a fraction of the resources. With this, you'd only need to break down a single solar system for resources rather then the dozens that would be needed for mining an area of space that large to a sufficient density to meaningfully deter an intruder.