Best answered by saying, and it also does in the film, that to Picard, the Borg were his White Whale, even goes as far as quoting Moby Dick in the film, and he gets referred to as Captain Ahab, who also took down his own crew, just to kill the white whale which took off his leg.
That's one thing I really liked about First Contact, it was a more personal thing with Picard - we've always seem him as a head strong person who you would follow into any battle, but this time around his obsession with them got the better of him. It was interesting to see him approach his White Whale and how he would handle it on that
ship with that
In the end he wasnt suited for the task, and Starfleet were right to keep him away from the goings on, but made for a good story to tell, watching a great captain fight his deamons.
And as usual, Worf was right!
It wasn't mentioned anywhere else - from what I have seen/read - but it could be argued the ends justified the means - Borg Queen dead and the past was fixed.
As it happens, Stewart was in a TV movie of Moby Dick around 1998, wasn't as good as the 1956 version it has to be said.