My biggest gripe about Section 31 when i was watching DS9 was it was completely counter to Roddenberry's vision of the future. While I was not opposed to an organization like Section 31 exisiting. The Romulans have the black ops Tal Shiar, and the Romulan military, civillians and other governments know about them. The Obsidian Order was black ops for the Cardassians, and again other governments knew about them. No one outside select few Star Fleet officers who have had interactions with Section 31 and possibly the entire Star Fleet Admiralty and Star Fleet Command knowsabout Section 31. Why so secretive? The fact that the Star Fleet Command would not confirm nor deny it's existence in DS9 'Inquisition' is very telling. While at the time I dismissed the line as writers trying to sound cool using a military phrase usually reserved for secrets and kills, but now after watching Enterprise and comparing Harris' and Sloan's actions i think I understand what Section 31 is.
Section 31 is an organization that acts to preserve and protect humanity. Not the Federation, but humanity. It's in the Earth Star Fleet charter in ENT, all Section 31 members are human we've seen, they are willing to take extreme actions such as genocide of an entire species to win a war, murder and extortion are not above them, and Star Fleet doesn't lift a finger to reprimand them for any of it.
I think fans would be more comfortable with Section 31 if there were public and not a cloak and dagger organization under Star Fleet. Star Fleet Command can say yes they exist but what they do is classified. Like the CIA and MI6. We know they infiltrate terrorist organizations, we know they use drones that kill the civilian populations of countries each occupy, and we know they lead assassinations against nuclear scientists in Iran and other countries. That's Section 31 in the Trekverse.