It’s not as if the Burn expunged all records of Klingon-Federation relations and the Federation had to rebuild from illuminated manuscripts copied by monks.

No, but I don't think there's any era that we've seen in which the Federation would stage an act of aggression as a diplomatic overture. Even in this episode, no one seemed sure it was going to work (and it may not have, were it not for Ake's personal connection to Obel).

the solution was that obvious.

I do agree - they probably telegraphed it a little too hard.