Because no one remembers a damn thing about the Orion pirates who only appeared in the animated series. and personally "pirates" are not a noticeable threat to any organized military force historically.
I agreed with this at first, but then I realized that Ulysses, epically, and Napoleon, historically, were both just that at some points in their lives.
I thought Starfleet was infamous for not being an organized military force? Pirates don't have to threaten the entirety of Starfleet anyway, they just have to threaten the protagonists. Especially now, with a lot of the fleet having been destroyed by a time-traveling Romulan miner, piracy is bound to be a concern.
A pirate story in the Trekverse isn't hard to conjure. Just have the pirates operate primarily outside of Federation space, but with occasional incursions. Have an independent planet petition the Federation and Klingons for help, let the planet's leaders manipulate both sides while the pirates induce mayhem. You could get a good story from that. Starfleet sends the Enterprise but not a complete task force because they are concerned about accidental war with the Klingons, etc.
Star Trek: Privateer? I still want to see Enterprise up against the Millenium Falcon... Make it happen, Abrams!
In the Star Trek screenplay I wrote, I had pirates (in this case, Yridians) disrupting Federation shipping near a non-aligned planet being courted by both the Klingons and the Federation. The Federation sends the Enterprise (with her new captain, Jim Kirk) to stop the pirates and to find out whether the Klingons are behind them. They're not, as it turns out, though the Klingons do use the attacks to their own political advantage. (The weapons the pirates are stealing are being used to instigate war between the Federation and the Klingons.) I think the writers for the JJVerse Trek might've read my script at some point; there are A LOT of plot point similarities with both Star Trek and Star Trek Into Darkness.
I've never fleshed out a Trek story on any level of detail, but all of the ideas I've had for Trek stories take place in that sort of gray zone -- the edges of Federation space, the edges of StarFleet ethics, etc. I like stories in which the characters are forced to reflect on who they really are and whether that's compatible with what they have to do in order to get through an existential threat.
They are an organized military force by any objective analysis of on screen evidence. Regardless of what they call themselves. The Israeli armed forces are called the "Israeli Defense Force" (ironically in Star Trek the Klingon fleet uses a similar name) yet virtually all of the IDF's military operations are OFFENSIVE in nature So a military force can call itself the Legion of Committed Pacifists but that doesn't change what it is. Starfleet is a military force that explores a lot of the time (as regular military forces on Earth have done in the past).
At this point in the JJVerse, they are about to embark on the first 5 year mission. The Enterprise, all alone. You think a fleet of Orion Pirates out in the middle of nowhere wouldn't pose a threat to them? Or that Starfleet could send reinforcements in time to be of any help?