It is amusing (or annoying, whichever you prefer) that when Geordi confirms there was a major problem with the Klingons and something happened involving the Enterprise, Picard asks no further questions before boarding the shuttlecraft. Maybe it was designed to be one of those implied, offscreen moments where Geordi and Worf inform him about the Enterprise's destruction after the shuttle takes off, but it just looks a little awkward for Picard not to say anything else.
Maybe that's a significant part of the reason why it's not in the final edit of the film. It just isn't a very good or well-designed scene.
Horrible deleted scene.
The natural reaction for Picard would've been the obvious, "What do you mean? What the hell happened?"
Yep. I'd like to know if there would even be a good way to write that scene in the first place, given all that just happened. Who speaks first? Does Picard tell Geordi and Worf about Kirk, and they have to interrupt him to tell him about the Enterprise? Do they break the news to him before he can say anything? If so, in terms of the story, it certainly overshadows Kirk's death in a hurry.
However, not really getting to see Picard's initial reaction to losing the Enterprise was bit of a loss. When we see him on the wreckage of he bridge, he seemed sanguine about it all. Almost as if, "Oh, well." There will be other Enterprises.
Indeed, in that last scene with Riker and Picard, it would've been nice for Picard to have mentioned Kirk in some way, maybe in response to a question Riker asks about Kirk. After all, there may be other ships named Enterprise, but there was only one James T. Kirk.