As regards the range of options open to Spock at that time, the writers have established a set of limitations for the transporter - largely unwittingly, through omissions, but still in a consistent manner.
A key feature of the Federation transporter, preserved in Abramsverse, is getting blocked by things between A and B. Sheer bedrock is one of those things - even without unobtainium in it, between two kilometers of it (TNG "Bloodlines") and a couple of hundred ("Return to Tomorrow") prevents transporting. This means the transporter is blocked by the horizon.
How far the horizon is depends on how high the starship hovers ("orbits", in the aeroplane sense) above the spot, then. Nero was practically kissing the surface. Pike parked his starship in a spot to match. And that spot was apparently in the middle of nowhere in Vulcan terms, so that no small craft would ascend to challenge Nero's extremely vulnerable drill - nicely befitting the idea of Sarek's mansion being where the local weirdos with their ancient fighting arenas hide from the reasonable folks, and where a rebellious kid can take a midnight walk across the most desolate desert of the planet.
Making the transporter reach other Vulcans once Nero's drill stopped jamming things would require Spock to raise the ship to a higher position, then (and he could never hope to reach most of the globe anyway, not being at liberty to leave the area of the Sarek mansion, aka the Doomsday Bunker of the Elders as per the presence of Sarek and Amanda there).
It's like if Indiana Jones suddenly drove through Auschwitz, only for the rest of the movie to continue as if that never happened. Yeah, theoretically that happened at the same time. But it would tonally be waaay of for that kind of movie.
Hmm. To nitpick, at the time the Joneses were taking their motorbike tour over the alps and getting Hitler's autograph, the Nazis were a bunch of goose-stepping clowns whose greatest claim to atrocity was their dress sense. And this no doubt was
not by accident: the makers of the movie would be thinking in the very terms of harmless youthful fun in the long summers before the one during which everybody had to grow up.
This doesn't work in the Trek context, where we are deprived of the knowledge that things will get much worse in the immediate future anyway and the loss of a few zillion is peanuts. Doubly so in the Abramsverse, where any knowledge of the fictional future would be negated by the changing of timelines! But we do know the Trek universe in every timeline is a dark place, where entire star systems can wink out at random and the death of billions is but a setup for forty-five minutes or so of suspense, with no particular consequences. The loss of Vulcan doesn't appear much different from the loss of, say, Maluria... Except for one of the regulars being a Vulcan but none being Malurian,
Timo Saloniemi