Those white pulses were Captain Robau's first choice for meeting the Nero threat, though.
No, they were not used at all while Robau was on board the Kelvin... or, for that matter, while he was alive
. Both times Narada fires on them, their missiles are (partially) intercepted by sweeping red phaser beams. The torpedo cannons aren't deployed until immediately after Robau was killed.
We might speculate that the pulses are an old-fashioned CIWS system
They're not. They were never used against Narada's missiles, and in fact we have no visual record of them successfully intercepting one. The trajectories of the pulses appear to be concentrated directly on the Narada, and immediately before Kirk begins his suicide run we see them focussing all of their fire in a single direction, evidently directly towards the center of the Narada's hull, at a time when the phasers are still sweeping laterally, screening the shuttles' escape.