My theory is that there's something wrong or dangerous with the use of Higg's particles as an energy source. Perhaps it eventually leads to a
False Vacuum Collapse or something, and the Antagonists target any civilization that uses it.
Given the reckless abandon with which the Antagonists use Higgs themselves, that seems rather unlikely.
If the Antagonists are engaging in an enforcement action, it is likely to be about the Valkyrie Cores. The pattern of events makes sense, broadly. First, Impact occurs, bringing with it some manner of dimensional portal in the form of the Breaches. At the same time, scattered debris from Impact contains the Cores. Given that we do not know what an efficient, long range, FTL system is like in this setting, the fifty some years that it took for the first Antags to arrive could well be in line with the lag on communications for the Impact event to be discovered and a response force organized to retrieve the Cores.
This theory pins the Valkyrie Cores as being a sort of Lost Logia (Nanoha term for what amounts to hypertech of unknowable function with potentially disastrous consequences for use). I do not think this theory is particularly likely.
The Antagonists of Knight Run are an interesting kettle of fish, because their origin and general motivation remains a mystery* across all the bits that are translated into English. My own theory for Knight Run is that the Antagonists of that setting are a runaway automated warfare system, of a similar nature to what A-10's project was aiming for. Still, for all that it fits, I do hope that for BAHHSCQ there is something else motivating the Antagonists.
My familiarity with Muv-Luv is insufficient to hazard a guess as to the enemies therein's motivation, and how probable or applicable it would be.
The JAM of Yukikaze, were interested in learning about/from the Humans of that setting. There are many parallels to the backstory of Yukikaze in BAHHSCQ, but my gut feeling says no to this thought.
*Pray's motivations, while clearly spelled out, do not fit the rest of the Antagonists
