The problem is, none of ENT's encounters is a very good case for observing a policy of covertly spying the other side before contact. And that's the policy that Picard tries to advocate in "First Contact".
If humans had sent infiltrators surgically altered to resemble Klingons to the Klingon worlds before "Broken Bow", how would matters have been improved? Archer would still have ignored Klingon sensibilities and would have shipped Klaang back home. He would still have sided with the refugees in "Judgment", and with the victims in "Marauders". Duras would still have had a feud with him.
And it's not as if "Broken Bow" were a real first contact for both sides, as Klaang's species was already starfaring and had access to all sorts of interstellar information and rumors, no doubt including bits on humans. It would fit the bill much better if, say, Vulcans descended on the Klingon homeworld in the 18th century and, out of ignorance rather than bullheadedness, committed some sort of a grave faux pas in their quest of advocating Surakianism, after which the Klingons launched an interstellar jihad that made them an important interstellar menace for the first time.
Of course, "fitting the bill" is something that shouldn't be our responsibility. Picard was making a sales pitch, and he could have taken liberties with truth, only telling that side of the story that supported his sale of covert surveillance.
Timo Saloniemi