Wait, do they?
Once free, what Bourne wants most of all, is to be left alone. He tells them this again and again. Yet time and time again the CIA and the secret assassin program insist on dragging this one-man death machine back into their lives. Why? What good ever comes from it?
You could say that the issue was secrecy, but Bourne could have exposed everything at any given moment just by going to the press, and he didn't. We know why, too -- Bourne has dirty laundry of his own (remember he was an assassin, and had killed multiple dudes in shady assassination operations). Can you imagine the relief when they found out that he just wants to go away somewhere and bang his hot German girlfriend without a care in the world? Let him!
Just let the man retire with Lola. What's the big hoo-hah?
But, no. They just can't let the guy go.
Let's look at the most inexplicable example. In the third film, it comes out that the main bad guy (Deputy Director of the CIA, Ward Abbott) is under investigation. It turns out that he had stolen money from the CIA in the past. He finds out that a trade is being made by the CIA for evidence that would incriminate him.
So, he hires some assassin to ambush the trade, kill everyone involved, and then plant Jason Bourne's fingerprints in order to frame him for it. He then sends the assassin after Bourne to kill him (SPOILER: This fails).
But also don't put all your chips on a near-sighted sniper