Since Spock knows of Kirk's altered past, and since he cannot travel back in time (stuck on Delta Vega), it would be obvious to him that things cannot be changed.
The fact that Spock would have done anything to save Vulcan if he could, and that it exists in the future he came from, tells me that he knows he cannot save it.
The problem with the "writers' intent" explanation is that (A) their theory of how Trek time-travel works is dicta, coming more from interviews than from anything in the film, and (B) it's incompatible with essentially every other Trek time-travel story we've ever seen.
And since we are talking time travel here, it's kinda beside the point that Spock couldn't travel further back to correct the divergence while he was trapped on Delta Vega. Once he got off
it, he certainly had both the knowledge and the means.
He's currently in a timeline different from the one he originated in: he knows that. But when he and Kirk were standing in front of the Guardian of Forever in "City" and suddenly realized that they were an anomaly in a universe wherein the Federation had never existed, did they say "oh, well, those are the breaks" or go back to undo the change? In "Yesteryear," when he discovers his own life history has been altered, does he leave it be or go back to correct it?
(Heck, for that matter (it's not Spock, but still relevant to the overall paradigm), in "Yesterday's Enterprise," when Picard is informed by Guinan that "something's wrong" about their timeline after a ship from 20 years prior pops up, even though he remembers every moment of his timeline as legitimate
, Picard sends that ship back to correct the divergence.)
SOP within the Federation, from all available evidence, has always been to assume that there's a single "primary" timeline that can be but shouldn't be altered, and to endeavor to keep it on course.