I cannot for the life of me remember the name of these things, though I just finished playing.
Anyway... they're the installations that add AIP each but knock it down by a much bigger amount if you kill all four (effectively giving you -40 AIP).
Two things that are, I'm sure, completely intended behavior, but which make destroying them unhelpful/Very Bad:
1) As you destroy each of them, your AIP goes up incrementally, which might bring your AI Mark level up by one (especially if it's at 0 or 1) before you've killed all four. Since Mark level doesn't decrease when AIP goes down, you've just shot yourself in the foot, since changes in Mark level are much more impactful than a meager 40 AIP.
2) If you're down at the floor of your AIP, destroying all four centers will actually INCREASE your current AIP, because total AIP goes up with each kill until you've hit all 4 (and the AIP floor goes up when your total AIP goes up). Since it's not possible to murder all 4 of them on the exact same frame, you WILL gain total AIP and floor AIP no matter what.
I'm sure this is intended behavior. But it's both a) annoying and b) not mentioned in any tool tips. (Not sure how easy it would be to explain the problem in a tool tip...)
I suppose I could knock out some math and get a real answer to my hypothesis, but I SUSPECT that there are very few circumstances in which knocking out the 4 centers is a Good Idea. Most of the time it's just going to bite you in the ass, at the very least because of the AIP floor increase. No matter what, your floor is going to go up. Not a fan of that.
Suggested solution: once you kill all 4 centers, both your current AIP and your total AIP go down by (net) 40, and ideally your mark level goes down if you go back under the threshold.
Otherwise it just seems to be a gameplay element that is best honored in the avoidance.