I would like to think that Starfleet doesn't "need" something like Section 31, and that Starfleet's official intelligence department would be sufficient for the job of, ya know, gathering intel, without resorting to things like assassinations, stealing technology (except in "The Enterprise Incident." It's okay when Kirk does it), kidnapping anybody, or anything shady like that.
Yet here we are.

So anyway, Section 31 goes from being a secret cabal operating in the shadows in the pre-Federation days of ENT, to operating more openly as some kind of elite commando group in ST-Disco, then eventually being booted so far back into the shadows that none of the Starfleet officers on DS9 had ever heard of them.
My pet theory, which I came up with just now off the top of my head, is that the "Section 31" we see in CBS Trek, and even in ST Into Darkness, isn't actually the
real Section 31 which hides in the shadows. Not even all of Starfleet Command knows about it. So some gung-ho, paranoid admiral such as Marcus in the Kelvin timeline, or somebody similar in the Prime timeline, is unaware of its existence, and sees this big "extraordinary threat" situation on the galactic scene and turns to the other admirals and says, "Hey, we've got this technicality in Article 14, Section 31 of the Starfleet Charter! Let's use that to commission a new elite black ops division that won't be limited by the official rules. Look how brilliant I am to have come up with this idea all on my own!" ...unaware that there is somebody behind the scenes like Harris or Sloan who was just about to try to make contact with their mole in Starfleet Command. And said mole decides it would be prudent
not to pipe up and respond, "Well, actually we've already got a, um, never mind."
Kor