How is Picard not going completely overboard in that scene?
I think your grading Star Trek Into Darkness on a Modern Trek scale. The original show had big bombastic emotional characters. What we see on the screen fits perfectly with the Star Trek I grew up with.
Picard does go overboard, he reaches this emotional climax but then finally realises what is happening to him. The scene's best bit is when he simmers down. Whereas in the nuTrek's style, Picard smashes that phaser against the display and then we cut to some action scene or climatic development. That would have been JJ Abram's approach, once an emotional climax has been reached let's hurtle to the next action scene or over-dramatic moment.
And yes I grew up with modern Trek, it's the only Star Trek I watch. I have seen bits and bobs of TOS and it is a product of its time. It was Star Trek in its infancy and a prototype in using a sci-fi drama to explore social issues, so we can forgive any such flaws or weird moments.
But the new Trek films are supposed to be about reinventing the franchise, acknowledging the original series whilst taking elements from TNG and DS9 (where Star Trek developed its maturity). The 2009 Star Trek film did this pretty well, but STID seems several steps backwards and if anything is a devolution into the Star Wars genre. I think Star Trek should stop worrying about being relevant and stop trying to compete with action blockbusters (it is not an action or science fantasy franchise!). If the story and the characters are great then Star Trek can still retain its identity and still be a little nerdy and ponderous.
If a movie like Inception can be made and make hundreds of millions in the box office, and Inception is as weird as they come and
it taxes the audience's brain which STID sadly doesn't, then why should Star Trek have to come down to the low standards of today's films? Star Trek did not develop through avoiding risks; which is why VOY and ENT lead to the franchise's demise.