I don't think it defeats the purpose since we know other organizations like the Tal Shiar and Obsidian Order function just fine. I think it morally corrupts the Federations "advertised" principles about freedom and enlightenment. Take that away and what makes the Fed and Star Fleet any different from The Romulan Star Empire, TOS Klingons, Cardassian Union, Breen or Dominion? Nothing. The Fed is just as cut throat and ruthless as any of them and advanced technology and pursuit of enlighten like Roddenberry envision for his series completely disappears. That what I think fans don't like about it. Yes Star Fleet is a military. However fans don't like the idea of Trek's military keeping company with Stargate's, NuBSG, and even our modern militaries in western countries.
Unfortunately this ideal is impossible in practice but easy to preach and by extension completely subverts Roddenberry's utopian future. It's a work in progress and it's something writers could write about. Season 1 Picard was probably given a Star Fleet manifesto about preaching points to his first contacts about enlightened society.
Now i think in the books Section 31 is credited or at least alluded to be responsible for a number of things we've seen throughout Trek history.
Kirk and Spock's actions in TOS "The Enterprise Incident" being under orders from the Federation (we can assume Star Fleet started the conversation) to steal the cloaking device. Kirk even states his unusal behavior and entering the Neutral Zone was to "keep the Enterprise and Federation off the hook".
TNG's "Pegasus" with the phasing cloak. Sanctioned by Star Fleet Command to be carried out by then Capt Pressman who was later promoted to Admiral.
TNG's "Insurrection" with Admiral Doughtery sanctioning the removal of the Ba'ku to get technology for the regenerative properties of their planet and using cloaked Federation ships and working with a known Dominion ally during the Dominion War.
There are a few others but I can't think of them off the top of my head.